diff --git a/packages/downgrader/src/v3.1-to-v3.0.ts b/packages/downgrader/src/v3.1-to-v3.0.ts
index 7f8df71..f426bd4 100644
--- a/packages/downgrader/src/v3.1-to-v3.0.ts
+++ b/packages/downgrader/src/v3.1-to-v3.0.ts
@@ -369,7 +369,9 @@ function losesRestriction(
       return !(
         names === true ||
         (isRecord(names) &&
-          Object.entries(names).every(([name, item]) => name === 'type' && item === 'string'))
+          Object.entries(names).every(
+            ([name, item]) => item === undefined || (name === 'type' && item === 'string'),
+          ))
       )
     }
     case 'unevaluatedProperties':
@@ -486,7 +488,9 @@ function valueType(value: unknown): string | undefined {
 
 function isMediaTypeOnly(value: unknown): boolean {
   return (
-    isRecord(value) && Object.keys(value).length === 1 && typeof value.contentMediaType === 'string'
+    isRecord(value) &&
+    typeof value.contentMediaType === 'string' &&
+    Object.entries(value).every(([key, item]) => key === 'contentMediaType' || item === undefined)
   )
 }
 
diff --git a/packages/downgrader/tests/v3.1-to-v3.0.test.ts b/packages/downgrader/tests/v3.1-to-v3.0.test.ts
index eb2b290..34a585a 100644
--- a/packages/downgrader/tests/v3.1-to-v3.0.test.ts
+++ b/packages/downgrader/tests/v3.1-to-v3.0.test.ts
@@ -1073,6 +1073,23 @@ describe('unusual input', () => {
     ])
   })
 
+  it('treats keys holding undefined as missing when deciding what to drop or loosen', () => {
+    expect(
+      downgradeSchemaV31ToV30({
+        type: 'string',
+        anyOf: [{ contentMediaType: 'image/png', description: undefined }],
+      }),
+    ).toEqual({ type: 'string' })
+    expect(
+      downgradeSchemaV31ToV30({
+        oneOf: [
+          { type: 'object', propertyNames: { type: 'string', description: undefined } },
+          { type: 'string' },
+        ],
+      }),
+    ).toEqual({ oneOf: [{ type: 'object' }, { type: 'string' }] })
+  })
+
   it('tolerates malformed input without throwing', () => {
     const doc = {
       openapi: '3.1.2',