diff --git a/src/mcp/server/streamable_http.py b/src/mcp/server/streamable_http.py
index aa99e7c88..43ec05fdd 100644
--- a/src/mcp/server/streamable_http.py
+++ b/src/mcp/server/streamable_http.py
@@ -426,10 +426,10 @@ async def _validate_accept_header(self, request: Request, scope: Scope, send: Se
                 )
                 await response(scope, request.receive, send)
                 return False
-        # For SSE responses, require both content types
-        elif not (has_json and has_sse):
+        # For SSE responses, require at least one supported content type
+        elif not (has_json or has_sse):
             response = self._create_error_response(
-                "Not Acceptable: Client must accept both application/json and text/event-stream",
+                "Not Acceptable: Client must accept application/json or text/event-stream",
                 HTTPStatus.NOT_ACCEPTABLE,
             )
             await response(scope, request.receive, send)
diff --git a/tests/issues/test_1363_race_condition_streamable_http.py b/tests/issues/test_1363_race_condition_streamable_http.py
index db2a82d07..4d2082ac4 100644
--- a/tests/issues/test_1363_race_condition_streamable_http.py
+++ b/tests/issues/test_1363_race_condition_streamable_http.py
@@ -137,7 +137,7 @@ async def test_race_condition_invalid_accept_headers(caplog: pytest.LogCaptureFi
 
         # Suppress WARNING logs (expected validation errors) and capture ERROR logs
         with caplog.at_level(logging.ERROR):
-            # Test with missing text/event-stream in Accept header
+            # Test with only application/json in Accept header (valid — single supported type)
             async with httpx.AsyncClient(
                 transport=httpx.ASGITransport(app=app), base_url="http://testserver", timeout=5.0
             ) as client:
@@ -145,14 +145,14 @@ async def test_race_condition_invalid_accept_headers(caplog: pytest.LogCaptureFi
                     "/",
                     json={"jsonrpc": "2.0", "method": "initialize", "id": 1, "params": {}},
                     headers={
-                        "Accept": "application/json",  # Missing text/event-stream
+                        "Accept": "application/json",
                         "Content-Type": "application/json",
                     },
                 )
-                # Should get 406 Not Acceptable due to missing text/event-stream
-                assert response.status_code == 406
+                # Single supported Accept type is sufficient
+                assert response.status_code == 200
 
-            # Test with missing application/json in Accept header
+            # Test with only text/event-stream in Accept header (valid — single supported type)
             async with httpx.AsyncClient(
                 transport=httpx.ASGITransport(app=app), base_url="http://testserver", timeout=5.0
             ) as client:
@@ -160,12 +160,12 @@ async def test_race_condition_invalid_accept_headers(caplog: pytest.LogCaptureFi
                     "/",
                     json={"jsonrpc": "2.0", "method": "initialize", "id": 1, "params": {}},
                     headers={
-                        "Accept": "text/event-stream",  # Missing application/json
+                        "Accept": "text/event-stream",
                         "Content-Type": "application/json",
                     },
                 )
-                # Should get 406 Not Acceptable due to missing application/json
-                assert response.status_code == 406
+                # Single supported Accept type is sufficient
+                assert response.status_code == 200
 
             # Test with completely invalid Accept header
             async with httpx.AsyncClient(
diff --git a/tests/shared/test_streamable_http.py b/tests/shared/test_streamable_http.py
index f8ca30441..a30d262c8 100644
--- a/tests/shared/test_streamable_http.py
+++ b/tests/shared/test_streamable_http.py
@@ -612,8 +612,7 @@ def test_accept_header_wildcard(basic_server: None, basic_server_url: str, accep
     "accept_header",
     [
         "text/html",
-        "application/*",
-        "text/*",
+        "image/png",
     ],
 )
 def test_accept_header_incompatible(basic_server: None, basic_server_url: str, accept_header: str):
@@ -630,6 +629,28 @@ def test_accept_header_incompatible(basic_server: None, basic_server_url: str, a
     assert "Not Acceptable" in response.text
 
 
+@pytest.mark.parametrize(
+    "accept_header",
+    [
+        "text/event-stream",
+        "application/json",
+        "application/*",
+        "text/*",
+    ],
+)
+def test_accept_header_single_type(basic_server: None, basic_server_url: str, accept_header: str):
+    """Test that a single supported Accept type is sufficient for SSE mode."""
+    response = requests.post(
+        f"{basic_server_url}/mcp",
+        headers={
+            "Accept": accept_header,
+            "Content-Type": "application/json",
+        },
+        json=INIT_REQUEST,
+    )
+    assert response.status_code == 200
+
+
 def test_content_type_validation(basic_server: None, basic_server_url: str):
     """Test that Content-Type header is properly validated."""
     # Test with incorrect Content-Type