--- a/src/testdir/test_vim9_assign.vim
+++ b/src/testdir/test_vim9_assign.vim
@@ -1821,10 +1821,31 @@ def Test_assign_lambda()
 enddef
 
 def Test_heredoc()
-  var lines =<< trim END # comment
-    text
+  # simple heredoc
+  var lines =<< trim END
+    var text =<< trim TEXT # comment
+      abc
+    TEXT
+    assert_equal(['abc'], text)
   END
-  assert_equal(['text'], lines)
+  v9.CheckDefAndScriptSuccess(lines)
+
+  # empty heredoc
+  lines =<< trim END
+     var text =<< trim TEXT
+     TEXT
+     assert_equal([], text)
+  END
+  v9.CheckDefAndScriptSuccess(lines)
+
+  # heredoc with a single empty line
+  lines =<< trim END
+     var text =<< trim TEXT
+
+     TEXT
+     assert_equal([''], text)
+  END
+  v9.CheckDefAndScriptSuccess(lines)
 
   v9.CheckDefFailure(['var lines =<< trim END X', 'END'], 'E488:')
   v9.CheckDefFailure(['var lines =<< trim END " comment', 'END'], 'E488:')
@@ -2642,51 +2663,68 @@ let g:someVar = 'X'
 " Test for heredoc with Vim expressions.
 " This messes up highlighting, keep it near the end.
 def Test_heredoc_expr()
-  var code =<< trim eval END
-    var a = `=5 + 10`
-    var b = `=min([10, 6])` + `=max([4, 6])`
-  END
-  assert_equal(['var a = 15', 'var b = 6 + 6'], code)
-
-  code =<< eval trim END
-    var s = "`=$SOME_ENV_VAR`"
-  END
-  assert_equal(['var s = "somemore"'], code)
-
-  code =<< eval END
-    var s = "`=$SOME_ENV_VAR`"
-END
-  assert_equal(['    var s = "somemore"'], code)
-
-  code =<< eval trim END
-    let a = `abc`
-    let b = `=g:someVar`
-    let c = `
-  END
-  assert_equal(['let a = `abc`', 'let b = X', 'let c = `'], code)
-
-  var lines =<< trim LINES
+  var lines =<< trim CODE
+    var s = "local"
+    var a1 = "1"
+    var a2 = "2"
+    var a3 = "3"
+    var a4 = ""
+    var code =<< trim eval END
+      var a = `=5 + 10`
+      var b = `=min([10, 6])` + `=max([4, 6])`
+      var c = "`=s`"
+      var d = x`=a1`x`=a2`x`=a3`x`=a4`
+    END
+    assert_equal(['var a = 15', 'var b = 6 + 6', 'var c = "local"', 'var d = x1x2x3x'], code)
+  CODE
+  v9.CheckDefAndScriptSuccess(lines)
+
+  lines =<< trim CODE
+    var code =<< eval trim END
+      var s = "`=$SOME_ENV_VAR`"
+    END
+    assert_equal(['var s = "somemore"'], code)
+  CODE
+  v9.CheckDefAndScriptSuccess(lines)
+
+  lines =<< trim CODE
+    var code =<< eval END
+      var s = "`=$SOME_ENV_VAR`"
+    END
+    assert_equal(['  var s = "somemore"'], code)
+  CODE
+  v9.CheckDefAndScriptSuccess(lines)
+
+  lines =<< trim CODE
+    var code =<< eval trim END
+      let a = `abc`
+      let b = `=g:someVar`
+      let c = `
+    END
+    assert_equal(['let a = `abc`', 'let b = X', 'let c = `'], code)
+  CODE
+  v9.CheckDefAndScriptSuccess(lines)
+
+  lines =<< trim LINES
       var text =<< eval trim END
         let b = `=
       END
   LINES
-  v9.CheckDefAndScriptFailure(lines, 'E1083:')
+  v9.CheckDefAndScriptFailure(lines, ['E1143: Empty expression: ""', 'E1083: Missing backtick'])
 
   lines =<< trim LINES
       var text =<< eval trim END
         let b = `=abc
       END
   LINES
-  v9.CheckDefAndScriptFailure(lines, 'E1083:')
+  v9.CheckDefAndScriptFailure(lines, ['E1001: Variable not found: abc', 'E1083: Missing backtick'])
 
   lines =<< trim LINES
       var text =<< eval trim END
         let b = `=`
       END
   LINES
-  v9.CheckDefAndScriptFailure(lines, 'E15:')
+  v9.CheckDefAndScriptFailure(lines, ['E1015: Name expected: `', 'E15: Invalid expression: "`"'])
 enddef
 
-
-
 " vim: ts=8 sw=2 sts=2 expandtab tw=80 fdm=marker