diff --git a/CHANGES.rst b/CHANGES.rst
index 201f1d069..82f174dd3 100644
--- a/CHANGES.rst
+++ b/CHANGES.rst
@@ -37,6 +37,10 @@ Unreleased
   - It has a little more room for line numbers so that 4-digit numbers work
     well, fixing `issue 1124`_.
 
+- Improved the error message when combining line and branch data, so that users
+  will be more likely to understand what's happening, closing `issue 803`_.
+
+.. _issue 803: https://github.com/nedbat/coveragepy/issues/803
 .. _issue 1108: https://github.com/nedbat/coveragepy/issues/1108
 .. _pull request 1110: https://github.com/nedbat/coveragepy/pull/1110
 .. _issue 1123: https://github.com/nedbat/coveragepy/issues/1123
diff --git a/coverage/sqldata.py b/coverage/sqldata.py
index b28b83b4f..a150fdfd0 100644
--- a/coverage/sqldata.py
+++ b/coverage/sqldata.py
@@ -486,9 +486,9 @@ def _choose_lines_or_arcs(self, lines=False, arcs=False):
         assert lines or arcs
         assert not (lines and arcs)
         if lines and self._has_arcs:
-            raise CoverageException("Can't add lines to existing arc data")
+            raise CoverageException("Can't add line measurements to existing branch data")
         if arcs and self._has_lines:
-            raise CoverageException("Can't add arcs to existing line data")
+            raise CoverageException("Can't add branch measurements to existing line data")
         if not self._has_arcs and not self._has_lines:
             self._has_lines = lines
             self._has_arcs = arcs
diff --git a/tests/test_data.py b/tests/test_data.py
index fe37bd9e7..eac9c36fa 100644
--- a/tests/test_data.py
+++ b/tests/test_data.py
@@ -159,13 +159,15 @@ def test_ok_to_add_arcs_twice(self):
     def test_cant_add_arcs_with_lines(self):
         covdata = CoverageData()
         covdata.add_lines(LINES_1)
-        with pytest.raises(CoverageException, match="Can't add arcs to existing line data"):
+        msg = "Can't add branch measurements to existing line data"
+        with pytest.raises(CoverageException, match=msg):
             covdata.add_arcs(ARCS_3)
 
     def test_cant_add_lines_with_arcs(self):
         covdata = CoverageData()
         covdata.add_arcs(ARCS_3)
-        with pytest.raises(CoverageException, match="Can't add lines to existing arc data"):
+        msg = "Can't add line measurements to existing branch data"
+        with pytest.raises(CoverageException, match=msg):
             covdata.add_lines(LINES_1)
 
     def test_touch_file_with_lines(self):