diff --git a/src/RestrictedPython/RCompile.py b/src/RestrictedPython/RCompile.py
index 80e439c..d046076 100644
--- a/src/RestrictedPython/RCompile.py
+++ b/src/RestrictedPython/RCompile.py
@@ -83,6 +83,9 @@ def compile(self):
 def _compileAndTuplize(gen):
     try:
         gen.compile()
+    except TypeError as v:
+        return CompileResult(
+            None, (str(v),), gen.rm.warnings, gen.rm.used_names)
     except SyntaxError as v:
         return CompileResult(
             None, (str(v),), gen.rm.warnings, gen.rm.used_names)
diff --git a/src/RestrictedPython/compile.py b/src/RestrictedPython/compile.py
index c611db6..7f0d674 100644
--- a/src/RestrictedPython/compile.py
+++ b/src/RestrictedPython/compile.py
@@ -27,28 +27,22 @@ def _compile_restricted_mode(
         c_ast = None
         try:
             c_ast = ast.parse(source, filename, mode)
+        except (TypeError, ValueError) as e:
+            errors.append(str(e))
         except SyntaxError as v:
-            c_ast = None
             errors.append('Line {lineno}: {type}: {msg} in on statement: {statement}'.format(
                 lineno=v.lineno,
                 type=v.__class__.__name__,
                 msg=v.msg,
                 statement=v.text.strip()
             ))
-        try:
-            if c_ast:
-                policy(errors, warnings, used_names).visit(c_ast)
-                if not errors:
-                    byte_code = compile(c_ast, filename, mode=mode  # ,
-                                        #flags=flags,
-                                        #dont_inherit=dont_inherit
-                                        )
-        except SyntaxError as v:
-            byte_code = None
-            errors.append(v)
-        except TypeError as v:
-            byte_code = None
-            errors.append(v)
+        if c_ast:
+            policy(errors, warnings, used_names).visit(c_ast)
+            if not errors:
+                byte_code = compile(c_ast, filename, mode=mode  # ,
+                                    #flags=flags,
+                                    #dont_inherit=dont_inherit
+                                    )
     return CompileResult(byte_code, tuple(errors), warnings, used_names)
 
 
diff --git a/tests/test_compile.py b/tests/test_compile.py
index 7cf3879..c7a8201 100644
--- a/tests/test_compile.py
+++ b/tests/test_compile.py
@@ -3,6 +3,7 @@
 from RestrictedPython._compat import IS_PY2
 
 import pytest
+import RestrictedPython.compile
 
 
 @pytest.mark.parametrize(*compile)
@@ -18,6 +19,70 @@ def test_compile__compile_restricted_exec__1(compile):
     assert glob['a'] == 42
 
 
+@pytest.mark.parametrize(*compile)
+def test_compile__compile_restricted_exec__2(compile):
+    """It compiles without restrictions if there is no policy."""
+    if compile is RestrictedPython.compile.compile_restricted_exec:
+        # The old version does not support a custom policy
+        result = compile('_a = 42', policy=None)
+        assert result.errors == ()
+        assert result.warnings == []
+        assert result.used_names == {}
+        glob = {}
+        exec(result.code, glob)
+        assert glob['_a'] == 42
+
+
+@pytest.mark.parametrize(*compile)
+def test_compile__compile_restricted_exec__3(compile):
+    """It returns a tuple of errors if the code is not allowed.
+
+    There is no code in this case.
+    """
+    result = compile('_a = 42\n_b = 43')
+    errors = (
+        'Line 1: "_a" is an invalid variable name because it starts with "_"',
+        'Line 2: "_b" is an invalid variable name because it starts with "_"')
+    if compile is RestrictedPython.compile.compile_restricted_exec:
+        assert result.errors == errors
+    else:
+        # The old version did only return the first error message.
+        assert result.errors == (errors[0],)
+    assert result.warnings == []
+    assert result.used_names == {}
+    assert result.code is None
+
+
+@pytest.mark.parametrize(*compile)
+def test_compile__compile_restricted_exec__4(compile):
+    """It does not return code on a SyntaxError."""
+    result = compile('asdf|')
+    assert result.code is None
+    assert result.warnings == []
+    assert result.used_names == {}
+    if compile is RestrictedPython.compile.compile_restricted_exec:
+        assert result.errors == (
+            'Line 1: SyntaxError: invalid syntax in on statement: asdf|',)
+    else:
+        # The old version had a less nice error message:
+        assert result.errors == ('invalid syntax (<string>, line 1)',)
+
+
+@pytest.mark.parametrize(*compile)
+def test_compile__compile_restricted_exec__5(compile):
+    """It does not return code if the code contains a NULL byte."""
+    result = compile('a = 5\x00')
+    assert result.code is None
+    assert result.warnings == []
+    assert result.used_names == {}
+    if IS_PY2:
+        assert result.errors == (
+            'compile() expected string without null bytes',)
+    else:
+        assert result.errors == (
+            'source code string cannot contain null bytes',)
+
+
 EXEC_STATEMENT = """\
 def no_exec():
     exec 'q = 1'