diff --git a/packages/downgrader/src/v3.1-to-v3.0.ts b/packages/downgrader/src/v3.1-to-v3.0.ts
index 47a4e4a..207c925 100644
--- a/packages/downgrader/src/v3.1-to-v3.0.ts
+++ b/packages/downgrader/src/v3.1-to-v3.0.ts
@@ -962,7 +962,8 @@ function admitsNull(schema: unknown): boolean {
 // becomes. A target that holds such a pair, beside annotations that 3.0 may
 // drop, such as `$comment`, can become its own `$ref` in turn, so a loop of
 // them, which in 3.1 admits only null, would become `$ref`s that match
-// nothing. One that does not admit null keeps its pair.
+// nothing. One that does not admit null keeps its pair. A pair nested in the
+// target's `anyOf`, as `anyOf: [{ anyOf: [$ref, null] }, null]`, leads on too.
 function refAdmitsNull(ref: string, ctx: Context): boolean {
   const seen = new Set<string>()
   for (let next: string | undefined = ref; next !== undefined;) {
@@ -975,12 +976,29 @@ function refAdmitsNull(ref: string, ctx: Context): boolean {
     }
     seen.add(next)
     const { anyOf } = target as Record<string, unknown>
-    const others = Array.isArray(anyOf) ? anyOf.filter((branch) => !acceptsNull(branch)) : []
+    const others = Array.isArray(anyOf) ? nonNullBranches(anyOf) : []
     next = others.length === 1 ? getRef(others[0]) : undefined
   }
   return true
 }
 
+// Met again, around a cycle of objects, a union adds nothing.
+function nonNullBranches(branches: unknown[], seen = new Set<unknown[]>()): unknown[] {
+  if (seen.has(branches)) {
+    return []
+  }
+  seen.add(branches)
+  return branches.flatMap((branch) => {
+    if (acceptsNull(branch)) {
+      return []
+    }
+    const nested = isRecord(branch) ? (branch.anyOf ?? branch.oneOf) : undefined
+    return Array.isArray(nested) && nested.some(acceptsNull)
+      ? nonNullBranches(nested, seen)
+      : [branch]
+  })
+}
+
 // A `type` with no `nullable: true` beside it, in 3.1 or 3.0, rejects null.
 function rejectsNull(schema: unknown): boolean {
   if (!isRecord(schema) || schema.nullable === true) {
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 64d3d55..888e513 100644
--- a/packages/downgrader/tests/v3.1-to-v3.0.test.ts
+++ b/packages/downgrader/tests/v3.1-to-v3.0.test.ts
@@ -1374,6 +1374,26 @@ describe('downgradeSchemaV31ToV30', () => {
         A: { anyOf: [ref('B'), onlyNull] },
         B: { description: 'B', anyOf: [ref('A'), onlyNull] },
       })
+      // So does a pair nested in the target's union.
+      const nested = { anyOf: [{ anyOf: [ref('A'), onlyNull] }, onlyNull] }
+      expect(schemas({ A: { anyOf: [pair('A'), { type: 'null' }] } })).toEqual({ A: nested })
+      expect(schemas({ A: { anyOf: [{ oneOf: pair('A').anyOf }, { type: 'null' }] } })).toEqual({
+        A: nested,
+      })
+      expect(
+        schemas({
+          A: pair('B'),
+          B: { anyOf: [{ anyOf: [ref('A'), ref('B')] }, { type: 'null' }] },
+        }),
+      ).toEqual({ A: ref('B'), B: { anyOf: [{ anyOf: [ref('A'), ref('B')] }, onlyNull] } })
+      expect(schemas({ A: pair('B'), B: { anyOf: [false, ref('A'), { type: 'null' }] } })).toEqual({
+        A: ref('B'),
+        B: { anyOf: [{ not: {} }, ref('A'), onlyNull] },
+      })
+      // A cycle of objects ends the walk.
+      const cyclic: Record<string, any> = { anyOf: [{ type: 'null' }] }
+      cyclic.anyOf.unshift({ anyOf: [cyclic, { type: 'null' }] })
+      expect(schemas({ A: pair('B'), B: cyclic })?.A).toEqual(ref('B'))
     })
 
     it('merges a branch in full where a cycle meets it before its conversion is done', () => {