diff --git a/Lib/test/test_traceback.py b/Lib/test/test_traceback.py
--- a/Lib/test/test_traceback.py
+++ b/Lib/test/test_traceback.py
@@ -204,16 +204,23 @@ class SyntaxTracebackCases(unittest.Test
             obj = PrintExceptionAtExit()
         """)
         rc, stdout, stderr = assert_python_ok('-c', code)
         expected = [b'Traceback (most recent call last):',
                     b'  File "<string>", line 8, in __init__',
                     b'ZeroDivisionError: division by zero']
         self.assertEqual(stderr.splitlines(), expected)
 
+    def test_print_exception(self):
+        output = StringIO()
+        traceback.print_exception(
+            Exception, Exception("projector"), None, file=output
+        )
+        self.assertEqual(output.getvalue(), "Exception: projector\n")
+
 
 class TracebackFormatTests(unittest.TestCase):
 
     def some_exception(self):
         raise KeyError('blah')
 
     @cpython_only
     def check_traceback_format(self, cleanup_func=None):
@@ -843,16 +850,21 @@ class TestTracebackException(unittest.Te
         linecache.updatecache('/foo.py', globals())
         e = Exception("uh oh")
         c = test_code('/foo.py', 'method')
         f = test_frame(c, globals(), {'something': 1})
         tb = test_tb(f, 6, None)
         exc = traceback.TracebackException(Exception, e, tb)
         self.assertEqual(exc.stack[0].locals, None)
 
+    def test_traceback_header(self):
+        # do not print traceback header if exc_traceback is None
+        # see issue #24695
+        exc = traceback.TracebackException(Exception, Exception("haven"), None)
+        self.assertEqual(list(exc.format()), ["Exception: haven\n"])
 
 class MiscTest(unittest.TestCase):
 
     def test_all(self):
         expected = set()
         blacklist = {'print_list'}
         for name in dir(traceback):
             if name.startswith('_') or name in blacklist:
diff --git a/Lib/traceback.py b/Lib/traceback.py
--- a/Lib/traceback.py
+++ b/Lib/traceback.py
@@ -448,16 +448,17 @@ class TracebackException:
                 exc_value.__context__,
                 exc_value.__context__.__traceback__,
                 limit=limit,
                 lookup_lines=False,
                 capture_locals=capture_locals,
                 _seen=_seen)
         else:
             context = None
+        self.exc_traceback = exc_traceback
         self.__cause__ = cause
         self.__context__ = context
         self.__suppress_context__ = \
             exc_value.__suppress_context__ if exc_value else False
         # TODO: locals.
         self.stack = StackSummary.extract(
             walk_tb(exc_traceback), limit=limit, lookup_lines=lookup_lines,
             capture_locals=capture_locals)
@@ -556,11 +557,12 @@ class TracebackException:
         if chain:
             if self.__cause__ is not None:
                 yield from self.__cause__.format(chain=chain)
                 yield _cause_message
             elif (self.__context__ is not None and
                 not self.__suppress_context__):
                 yield from self.__context__.format(chain=chain)
                 yield _context_message
-        yield 'Traceback (most recent call last):\n'
+        if self.exc_traceback is not None:
+            yield 'Traceback (most recent call last):\n'
         yield from self.stack.format()
         yield from self.format_exception_only()