diff --git a/src/TraceClient/TraceClient.cs b/src/TraceClient/TraceClient.cs
index 7bf075c..dd3e2f1 100644
--- a/src/TraceClient/TraceClient.cs
+++ b/src/TraceClient/TraceClient.cs
@@ -137,7 +137,16 @@ public TraceClient(string baseUrl, string application, string version, string ke
             {
                 throw new ArgumentException("version is longer than " + MaxLength + " characters", "version");
             }
-            _endpoint = new Uri(baseUrl.Trim().TrimEnd('/') + "/api/metrics");
+            try
+            {
+                _endpoint = new Uri(baseUrl.Trim().TrimEnd('/') + "/api/metrics");
+            }
+            catch (UriFormatException malformed)
+            {
+                // UriFormatException is a FormatException, not an ArgumentException;
+                // rethrow so a malformed baseUrl fails the way the docs promise.
+                throw new ArgumentException("baseUrl is not a valid URL", "baseUrl", malformed);
+            }
             _application = application.Trim();
             _version = version.Trim();
             _key = key == null ? "" : key.Trim();
diff --git a/tests/TraceClient.Tests/TraceClientTest.cs b/tests/TraceClient.Tests/TraceClientTest.cs
index 582ac10..6dbd83f 100644
--- a/tests/TraceClient.Tests/TraceClientTest.cs
+++ b/tests/TraceClient.Tests/TraceClientTest.cs
@@ -274,6 +274,18 @@ public void Constructor_RejectsAMissingBaseUrlOrApplication()
             Assert.Throws<ArgumentException>(() => new TraceClient("http://x", "", "1.2.3"));
         }
 
+        [Fact]
+        public void Constructor_RejectsAMalformedBaseUrlWithAnArgumentException()
+        {
+            // Exactly ArgumentException, as documented -- not the UriFormatException
+            // underneath, which a caller catching ArgumentException would miss.
+            ArgumentException thrown = Assert.Throws<ArgumentException>(
+                () => new TraceClient("not a url", "MyGame", "1.2.3", key: "k"));
+
+            Assert.Equal("baseUrl", thrown.ParamName);
+            Assert.IsType<UriFormatException>(thrown.InnerException);
+        }
+
         [Fact]
         public void Constructor_RejectsAMissingOrOverlongVersion()
         {