diff --git a/pylabrobot/hamilton/star/driver/features/head96.py b/pylabrobot/hamilton/star/driver/features/head96.py
index 98d938f712b..9b1806bb95d 100644
--- a/pylabrobot/hamilton/star/driver/features/head96.py
+++ b/pylabrobot/hamilton/star/driver/features/head96.py
@@ -30,6 +30,10 @@
 from pylabrobot.hamilton.star.driver.features.head import Head, HeadConfiguration
 from pylabrobot.hamilton.star.driver.lld_mode import LLDMode
 from pylabrobot.hamilton.star.liquid_classes.mapping import get_star_liquid_class
+from pylabrobot.lib.liquid_handling.head_alignment import (
+  get_items_under_channels,
+  get_shift_with_channel_over,
+)
 from pylabrobot.lib.liquid_handling.mix import Mix
 from pylabrobot.resources.container import Container
 from pylabrobot.resources.coordinate import Coordinate
@@ -38,7 +42,7 @@
 from pylabrobot.resources.plate import Plate
 from pylabrobot.resources.resource import Resource
 from pylabrobot.resources.tip import Tip
-from pylabrobot.resources.tip_rack import TipRack, check_tip_racks_available, tip_origin
+from pylabrobot.resources.tip_rack import TipRack, TipSpot, check_tip_racks_available, tip_origin
 from pylabrobot.resources.volume_tracker import VolumeTracker, does_volume_tracking
 from pylabrobot.resources.well import Well
 
@@ -668,24 +672,30 @@ async def pick_up_tips(
     tip_pickup_method: Literal["from_rack", "from_waste", "full_blowout"] = "from_rack",
     minimum_height_command_end: Optional[float] = None,
     minimum_traverse_height_start: Optional[float] = None,
+    *,
+    channel: str = "A1",
+    tip_spot: str = "A1",
   ) -> None:
-    """Pick up a rack of tips on the whole head, as legacy's `pick_up_tips96`. `C0 EP`.
+    """Pick up tips from a rack on the head, as legacy's `pick_up_tips96`. `C0 EP`.
 
-    Head channel A1 goes to the centre of spot A1, at the spot's Z. Once the device has picked them
-    up, the tip in each spot is mounted on the shaft of the channel with the spot's index.
+    Head channel `channel` goes to the centre of spot `tip_spot`, at the spot's Z. Once the device
+    has picked them up, each channel over a spot holding a tip has that tip on its shaft. Channels
+    past the rack's edge come down beside it: what stands there is the caller's to keep clear.
 
     Args:
       tip_rack: a 96 tip rack. Spots without a tip give none.
-      offset: added to spot A1's centre, in mm.
+      offset: added to the spot's centre, in mm.
       tip_pickup_method: `from_rack` sends the dispensing drive down first, since the device does
         not; `from_waste` and `full_blowout` move the plunger up before mounting.
       minimum_height_command_end: in mm. `configuration.traversal_z_position` when None.
       minimum_traverse_height_start: in mm.
         `configuration.traversal_z_position` when None.
+      channel: the head channel placed over `tip_spot`, A1 to H12.
+      tip_spot: the spot `channel` is placed over, A1 to H12.
 
     Raises:
-      ValueError: If the rack does not have 96 spots or holds no tips, or a position cannot be
-        reached.
+      ValueError: If the rack does not have 96 spots, no channel is over a tip, a position
+        cannot be reached, or a channel is past the edge of a rack with a frame.
       TypeError: If its tips are not Hamilton tips.
       RuntimeError: If the driver was given no deck, or the head already carries tips.
     """
@@ -699,19 +709,29 @@ async def pick_up_tips(
     if tip_rack.num_items != 96:
       raise ValueError("Tip rack must have 96 tips")
     check_tip_racks_available(tip_rack.get_all_items()[:1], "pick up tips from")
+    tip_spots_under_channels = get_items_under_channels(tip_rack, channel, tip_spot)
+    # Past the rack's edge the head's body comes down over the rack's frame.
+    if None in tip_spots_under_channels and tip_rack.frame_height != 0:
+      raise ValueError(
+        f"{tip_rack.name!r} has a frame the head would hit unless channel A1 is over spot A1"
+      )
     tips = [
-      spot.tip_for_pickup() if not spot.tracks_tips or spot.tip is not None else None
-      for spot in tip_rack.get_all_items()
+      spot.tip_for_pickup()
+      if spot is not None and (not spot.tracks_tips or spot.tip is not None)
+      else None
+      for spot in tip_spots_under_channels
     ]
     prototypical_tip = next((tip for tip in tips if tip is not None), None)
     if prototypical_tip is None:
-      raise ValueError("No tips found in the tip rack.")
+      raise ValueError("No tips found under the head.")
     if not isinstance(prototypical_tip, HamiltonTip):
       raise TypeError("Tip type must be HamiltonTip.")
     tip_type_index = await self._driver.get_or_assign_tip_type_index(prototypical_tip)
 
-    location = tip_rack.get_item("A1").get_location_wrt(deck, x="c", y="c", z="b") + (
-      offset or Coordinate.zero()
+    location = (
+      tip_rack.get_item("A1").get_location_wrt(deck, x="c", y="c", z="b")
+      + get_shift_with_channel_over(tip_rack, channel, tip_spot, deck)
+      + (offset or Coordinate.zero())
     )
     traverse_z, end_z = self._resolve_tip_command_heights(
       minimum_traverse_height_start, minimum_height_command_end
@@ -760,12 +780,15 @@ async def drop_tips(
     offset: Optional[Coordinate] = None,
     minimum_height_command_end: Optional[float] = None,
     minimum_traverse_height_start: Optional[float] = None,
+    *,
+    channel: str = "A1",
+    tip_spot: str = "A1",
   ) -> None:
     """Drop the head's tips into a tip rack or anywhere else, as legacy's `drop_tips96`. `C0 ER`.
 
-    Into a tip rack, head channel A1 goes to the centre of spot A1, at the spot's Z, and each
-    channel's tip goes into the spot with its index. Anywhere else, the head is centred over the
-    resource, and the tips belong to nothing afterwards.
+    Into a tip rack, head channel `channel` goes to the centre of spot `tip_spot`, at the spot's
+    Z, and each channel's tip goes into the spot under it. Anywhere else, the head is centred over
+    the resource, and the tips belong to nothing afterwards.
 
     Args:
       resource: a 96 tip rack, or anything else, such as the trash.
@@ -773,19 +796,38 @@ async def drop_tips(
       minimum_height_command_end: in mm. `configuration.traversal_z_position` when None.
       minimum_traverse_height_start: in mm.
         `configuration.traversal_z_position` when None.
+      channel: the head channel placed over `tip_spot`, A1 to H12. A tip rack only.
+      tip_spot: the spot `channel` is placed over, A1 to H12. A tip rack only.
 
     Raises:
-      ValueError: If a tip rack does not have 96 spots, or a position cannot be reached.
+      ValueError: If a tip rack does not have 96 spots, a channel carrying a tip is not over a
+        spot, a position cannot be reached, or a channel is past the edge of a rack with a frame.
       RuntimeError: If the driver was given no deck.
     """
     deck = self._driver.deck
     if deck is None:
       raise RuntimeError("tip commands are placed from the deck; this driver was given none")
+    tip_spots_under_channels: List[Optional[TipSpot]] = []
     if isinstance(resource, TipRack):
       if resource.num_items != 96:
         raise ValueError("Tip rack must have 96 tips")
       check_tip_racks_available(resource.get_all_items()[:1], "drop tips into")
+      tip_spots_under_channels = get_items_under_channels(resource, channel, tip_spot)
+      # Past the rack's edge the head's body comes down over the rack's frame.
+      if None in tip_spots_under_channels and resource.frame_height != 0:
+        raise ValueError(
+          f"{resource.name!r} has a frame the head would hit unless channel A1 is over spot A1"
+        )
+      if self.resource is not None:
+        beside = [
+          shaft.name
+          for shaft, spot in zip(self.resource.get_all_items(), tip_spots_under_channels)
+          if shaft.has_tip() and spot is None
+        ]
+        if beside:
+          raise ValueError(f"channels {beside} carry a tip but are not over a spot of the rack")
       location = resource.get_item("A1").get_location_wrt(deck, x="c", y="c", z="b")
+      location += get_shift_with_channel_over(resource, channel, tip_spot, deck)
     else:
       location = self._position_centred_in(resource)
     location += offset or Coordinate.zero()
@@ -821,8 +863,8 @@ async def drop_tips(
             continue
           tip = shaft.release_tip()
           if isinstance(resource, TipRack) and isinstance(tip, Tip):
-            spot = resource.get_item(i)
-            if spot.tracks_tips:
+            spot = tip_spots_under_channels[i]
+            if spot is not None and spot.tracks_tips:
               spot.assign_tip(tip)
       await self._record_after_tip_command(command_error)
     await self.dispensing_drive_request_uL_position()
@@ -830,38 +872,41 @@ async def drop_tips(
   async def return_tips(self, **kwargs) -> None:
     """Put the head's tips back in the tip rack they were picked up from.
 
-    The rack is found from each tip's origin. Channels without a tip are skipped.
+    The rack, and the spot each channel stood over, are found from each tip's origin. Channels
+    without a tip are skipped.
 
     Args:
       kwargs: passed on to `drop_tips`.
 
     Raises:
       RuntimeError: If the driver was given no deck, the head is not modelled or carries no tips,
-        or a tip does not come from the spot with its channel's index in one tip rack on the deck.
+        or its tips did not all stand under their channels in one tip rack on the deck.
     """
     deck = self._driver.deck
     if deck is None:
       raise RuntimeError("tip commands are placed from the deck; this driver was given none")
     if self.resource is None:
       raise RuntimeError("the head is not modelled, so where its tips came from is not known")
-    tip_rack: Optional[TipRack] = None
-    for index, shaft in enumerate(self.resource.get_all_items()):
+    shafts = self.resource.get_all_items()
+    carrying = next((shaft for shaft in shafts if isinstance(shaft.tip, Tip)), None)
+    if carrying is None:
+      raise RuntimeError("No tips have been picked up.")
+    origin = tip_origin(cast(Tip, carrying.tip), deck)
+    if origin is None or not isinstance(origin.parent, TipRack):
+      raise RuntimeError(f"the tip on {carrying.name} did not come from a tip rack on the deck")
+    tip_rack = origin.parent
+    # Any one tip names the pick-up: its channel stood over the spot it came from.
+    channel = self.resource.get_child_identifier(carrying)
+    tip_spot = tip_rack.get_child_identifier(origin)
+    tip_spots_under_channels = get_items_under_channels(tip_rack, channel, tip_spot)
+    for shaft, spot in zip(shafts, tip_spots_under_channels):
       tip = shaft.tip
-      if not isinstance(tip, Tip):
-        continue
-      spot = tip_origin(tip, deck)
-      if spot is None or not isinstance(spot.parent, TipRack):
-        raise RuntimeError(f"{tip.name} on {shaft.name} did not come from a tip rack on the deck")
-      if tip_rack is None:
-        tip_rack = spot.parent
-      if spot.parent is not tip_rack or tip_rack.get_item(index) is not spot:
+      if isinstance(tip, Tip) and tip_origin(tip, deck) is not spot:
         raise RuntimeError(
-          f"{shaft.name}'s tip {tip.name} is not from spot {index} of {tip_rack.name}; the head "
-          "returns tips only to the one rack they were picked up from"
+          f"{shaft.name}'s tip {tip.name} did not stand under it in {tip_rack.name}; the head "
+          "returns tips only as it picked them up from one rack"
         )
-    if tip_rack is None:
-      raise RuntimeError("No tips have been picked up.")
-    await self.drop_tips(tip_rack, **kwargs)
+    await self.drop_tips(tip_rack, channel=channel, tip_spot=tip_spot, **kwargs)
 
   async def discard_tips(self, **kwargs) -> None:
     """Drop the head's tips into the deck's 96-head trash, whatever the model says it carries.
diff --git a/pylabrobot/hamilton/star/driver/features/head_tests.py b/pylabrobot/hamilton/star/driver/features/head_tests.py
index d746b60a286..59195a3e92e 100644
--- a/pylabrobot/hamilton/star/driver/features/head_tests.py
+++ b/pylabrobot/hamilton/star/driver/features/head_tests.py
@@ -158,7 +158,12 @@ class TestHead96Tips(unittest.IsolatedAsyncioTestCase):
 
   async def asyncSetUp(self):
     from pylabrobot.resources import set_tip_tracking
-    from pylabrobot.resources.hamilton import TIP_CAR_480_A00, hamilton_96_tiprack_300uL_filter
+    from pylabrobot.resources.hamilton import (
+      TIP_CAR_480_A00,
+      hamilton_96_tiprack_300uL_filter,
+      hamilton_96_tiprack_raised_core_ii,
+      hamilton_tip_300uL_filter,
+    )
 
     set_tip_tracking(True)
     self.addCleanup(set_tip_tracking, False)
@@ -171,6 +176,10 @@ async def asyncSetUp(self):
     self.head_resource = cast(NChannelPipette, self.head.resource)
     tip_car = TIP_CAR_480_A00(name="tip carrier")
     tip_car[1] = self.tip_rack = hamilton_96_tiprack_300uL_filter(name="tip_rack_01")
+    # A rack without a frame, which the head may be placed past the edge of.
+    tip_car[3] = self.frameless_tip_rack = hamilton_96_tiprack_raised_core_ii(
+      name="frameless_tip_rack", make_tip=hamilton_tip_300uL_filter
+    )
     self.deck.assign_child_resource(tip_car, track=1)
     self.sent: List[str] = []
     log = self.driver._log_exchange
@@ -244,6 +253,25 @@ async def test_tips_missing_from_a_rack_are_missing_from_the_head(self):
         self.assertFalse(any(shaft.has_tip() for shaft in shafts))
         self.tip_rack.fill()
 
+  async def test_a_channel_placed_over_a_spot_takes_only_the_tips_under_the_head(self):
+    # Channel H12 over spot D6: channels E7 to H12 stand over spots A1 to D6, the rest past the rack.
+    rack, shafts = self.frameless_tip_rack, self.head_resource
+    rack.get_item("A2").unassign_tip()
+    under = {
+      f"{'EFGH'[row]}{column + 7}": rack.get_item(f"{'ABCD'[row]}{column + 1}")
+      for row in range(4)
+      for column in range(6)
+    }
+    tips = {channel: spot.tip for channel, spot in under.items()}
+
+    await self.head.pick_up_tips(rack, channel="H12", tip_spot="D6")
+
+    # Channel A1 ends 6 columns left and 4 rows behind spot A1 (xs01179 yh4338): -54 mm X, +36 mm Y.
+    self.assertEqual(self.sent[-1], "C0EPxs00639xd0yh4698tt01wu0za2310zh2450ze2450")
+    for shaft in shafts.get_all_items():
+      channel = shafts.get_child_identifier(shaft)
+      self.assertIs(shaft.tip, tips.get(channel), channel)
+
   async def test_tips_dropped_in_the_trash_belong_to_nothing(self):
     await self.head.pick_up_tips(self.tip_rack)
     tips = [shaft.tip for shaft in self.head_resource.get_all_items()]
@@ -311,6 +339,33 @@ async def test_return_tips_drops_them_in_the_rack_they_came_from(self):
     self.assertEqual([spot.tip for spot in self.tip_rack.get_all_items()], tips)
     self.assertFalse(any(shaft.has_tip() for shaft in self.head_resource.get_all_items()))
 
+  async def test_a_drop_that_would_let_a_tip_go_beside_the_rack_is_refused(self):
+    await self.head.pick_up_tips(self.tip_rack)
+    self.sent.clear()
+    with self.assertRaisesRegex(ValueError, "carry a tip but are not over a spot"):
+      await self.head.drop_tips(self.frameless_tip_rack, channel="A1", tip_spot="A10")
+    self.assertEqual(self.sent, [])
+
+  async def test_a_rack_with_a_frame_takes_the_head_only_channel_a1_over_spot_a1(self):
+    with self.assertRaisesRegex(ValueError, "'tip_rack_01' has a frame the head would hit"):
+      await self.head.pick_up_tips(self.tip_rack, channel="H12", tip_spot="D6")
+    self.assertEqual(self.sent, [])
+    await self.head.pick_up_tips(self.frameless_tip_rack, channel="H12", tip_spot="D6")
+    self.sent.clear()
+    with self.assertRaisesRegex(ValueError, "'tip_rack_01' has a frame the head would hit"):
+      await self.head.drop_tips(self.tip_rack, channel="H12", tip_spot="D6")
+    self.assertEqual(self.sent, [])
+
+  async def test_return_tips_puts_them_back_under_the_channels_that_took_them(self):
+    rack = self.frameless_tip_rack
+    rack.get_item("A2").unassign_tip()
+    tips = [spot.tip for spot in rack.get_all_items()]
+    await self.head.pick_up_tips(rack, channel="H12", tip_spot="D6")
+    self.sent.clear()
+    await self.head.return_tips()
+    self.assertEqual(self.sent, ["C0ERxs00639xd0yh4698za2310zh2450ze2450"])
+    self.assertEqual([spot.tip for spot in rack.get_all_items()], tips)
+
   async def test_discard_tips_drops_them_in_the_96_trash(self):
     await self.head.pick_up_tips(self.tip_rack)
     self.sent.clear()
@@ -333,7 +388,7 @@ async def test_return_tips_refuses_tips_from_two_racks(self):
     shaft.release_tip()
     shaft.mount_tip(other_rack.get_item(5).tip_for_pickup())
     self.sent.clear()
-    with self.assertRaisesRegex(RuntimeError, "not from spot 5 of tip_rack_01"):
+    with self.assertRaisesRegex(RuntimeError, "did not stand under it in tip_rack_01"):
       await self.head.return_tips()
     self.assertEqual(self.sent, [])
 
diff --git a/pylabrobot/lib/liquid_handling/head_alignment.py b/pylabrobot/lib/liquid_handling/head_alignment.py
new file mode 100644
index 00000000000..79326f2d030
--- /dev/null
+++ b/pylabrobot/lib/liquid_handling/head_alignment.py
@@ -0,0 +1,51 @@
+"""Align a fixed-grid head with a grid of the same pitch: which item is under which channel.
+
+A head channel and the item of its name share a row and a column, so a tip rack or a plate of
+the head's size is the head's own grid. One channel placed over one item fixes the alignment.
+"""
+
+from typing import List, Optional, TypeVar
+
+from pylabrobot.resources import Coordinate, ItemizedResource, Resource
+
+T = TypeVar("T", bound=Resource)
+
+
+def get_items_under_channels(
+  grid: ItemizedResource[T], channel: str, item: str
+) -> List[Optional[T]]:
+  """The item under each head channel with `channel` over `item`, in channel order.
+
+  Args:
+    grid: a tip rack or a plate with the head's rows and columns.
+    channel: the head channel, e.g. A1.
+    item: the item it is placed over, e.g. A10.
+
+  Returns:
+    One entry per channel; None for a channel past the grid's edge.
+  """
+  over, under = grid.get_item(item), grid.get_item(channel)
+  row_shift = grid.get_child_row(over) - grid.get_child_row(under)
+  column_shift = grid.get_child_column(over) - grid.get_child_column(under)
+  items: List[Optional[T]] = []
+  for named in grid.get_all_items():
+    row = grid.get_child_row(named) + row_shift
+    column = grid.get_child_column(named) + column_shift
+    inside = 0 <= row < grid.num_items_y and 0 <= column < grid.num_items_x
+    items.append(grid.get_item((row, column)) if inside else None)
+  return items
+
+
+def get_shift_with_channel_over(
+  grid: ItemizedResource[T], channel: str, item: str, deck: Resource
+) -> Coordinate:
+  """How far head channel A1 stands from item A1 with `channel` over `item`, in deck mm.
+
+  Args:
+    grid: a tip rack or a plate with the head's rows and columns.
+    channel: the head channel, e.g. A1.
+    item: the item it is placed over, e.g. A10.
+    deck: the deck the grid stands on.
+  """
+  over, under = grid.get_item(item), grid.get_item(channel)
+  return over.get_location_wrt(deck) - under.get_location_wrt(deck)
diff --git a/pylabrobot/lib/liquid_handling/head_alignment_tests.py b/pylabrobot/lib/liquid_handling/head_alignment_tests.py
new file mode 100644
index 00000000000..21469427ca2
--- /dev/null
+++ b/pylabrobot/lib/liquid_handling/head_alignment_tests.py
@@ -0,0 +1,36 @@
+"""Tests for aligning a fixed-grid head with a grid of the same pitch."""
+
+import pytest
+
+from pylabrobot.lib.liquid_handling.head_alignment import (
+  get_items_under_channels,
+  get_shift_with_channel_over,
+)
+from pylabrobot.resources import Coordinate, Resource
+from pylabrobot.resources.hamilton import hamilton_96_tiprack_300uL_filter
+
+
+def test_each_channel_stands_over_the_item_the_alignment_puts_under_it() -> None:
+  # Channel H12 over spot D6: channels E7 to H12 stand over spots A1 to D6, the rest past the rack.
+  rack = hamilton_96_tiprack_300uL_filter(name="tip_rack")
+  under = {
+    f"{'EFGH'[row]}{column + 7}": rack.get_item(f"{'ABCD'[row]}{column + 1}")
+    for row in range(4)
+    for column in range(6)
+  }
+
+  items = get_items_under_channels(rack, channel="H12", item="D6")
+
+  channels = [rack.get_child_identifier(spot) for spot in rack.get_all_items()]
+  assert items == [under.get(channel) for channel in channels]
+
+
+def test_channel_a1_is_shifted_by_the_rows_and_columns_between_the_two() -> None:
+  deck = Resource(name="deck", size_x=1000, size_y=600, size_z=0)
+  rack = hamilton_96_tiprack_300uL_filter(name="tip_rack")
+  deck.assign_child_resource(rack, location=Coordinate(100, 100, 0))
+
+  shift = get_shift_with_channel_over(rack, channel="H12", item="D6", deck=deck)
+
+  # 6 columns to the left and 4 rows behind, at the rack's 9 mm pitch.
+  assert (shift.x, shift.y, shift.z) == pytest.approx((-54.0, 36.0, 0.0))
diff --git a/pylabrobot/resources/hamilton/tip_racks.py b/pylabrobot/resources/hamilton/tip_racks.py
index 3fdf3e43197..5481a5f33ea 100644
--- a/pylabrobot/resources/hamilton/tip_racks.py
+++ b/pylabrobot/resources/hamilton/tip_racks.py
@@ -87,6 +87,7 @@ def hamilton_96_tiprack_ntr(
       name_prefix=name,
     ),
     with_tips=with_tips,
+    frame_height=0.0,
   )
 
 
@@ -117,6 +118,7 @@ def _hamilton_96_tiprack_raised(
       name_prefix=name,
     ),
     with_tips=with_tips,
+    frame_height=0.0,
   )