diff --git a/src/query-builder/insert-query-builder.ts b/src/query-builder/insert-query-builder.ts
index fc160ed14..f5d62d42d 100644
--- a/src/query-builder/insert-query-builder.ts
+++ b/src/query-builder/insert-query-builder.ts
@@ -235,12 +235,6 @@ export class InsertQueryBuilder<DB, TB extends keyof DB, O>
    * }))
    * ```
    */
-  values(insert: InsertObjectOrList<DB, TB>): InsertQueryBuilder<DB, TB, O>
-
-  values(
-    insert: InsertObjectOrListFactory<DB, TB>
-  ): InsertQueryBuilder<DB, TB, O>
-
   values(insert: InsertExpression<DB, TB>): InsertQueryBuilder<DB, TB, O> {
     const [columns, values] = parseInsertExpression(insert)
 
diff --git a/src/query-builder/update-query-builder.ts b/src/query-builder/update-query-builder.ts
index c43fe483e..184df8303 100644
--- a/src/query-builder/update-query-builder.ts
+++ b/src/query-builder/update-query-builder.ts
@@ -535,10 +535,8 @@ export class UpdateQueryBuilder<DB, UT extends keyof DB, TB extends keyof DB, O>
    * where "id" = $5
    * ```
    */
-  set(update: UpdateObject<DB, TB, UT>): UpdateQueryBuilder<DB, UT, TB, O>
-
   set(
-    update: UpdateObjectFactory<DB, TB, UT>
+    update: UpdateObjectExpression<DB, TB, UT>
   ): UpdateQueryBuilder<DB, UT, TB, O>
 
   set<RE extends ReferenceExpression<DB, UT>>(
diff --git a/test/typings/test-d/insert.test-d.ts b/test/typings/test-d/insert.test-d.ts
index d4804f477..125ed0e93 100644
--- a/test/typings/test-d/insert.test-d.ts
+++ b/test/typings/test-d/insert.test-d.ts
@@ -61,6 +61,17 @@ async function testInsert(db: Kysely<Database>) {
 
   expectType<InsertResult>(r5)
 
+  const r6 = await db
+    .insertInto('person')
+    .values((eb) => ({
+      first_name: 'fname',
+      age: 10,
+      gender: eb.ref('gender'),
+    }))
+    .executeTakeFirst()
+
+  expectType<InsertResult>(r6)
+
   // Non-existent table
   expectError(db.insertInto('doesnt_exists'))
 
diff --git a/test/typings/test-d/kysely-any.test-d.ts b/test/typings/test-d/kysely-any.test-d.ts
index b1468a722..729d529c3 100644
--- a/test/typings/test-d/kysely-any.test-d.ts
+++ b/test/typings/test-d/kysely-any.test-d.ts
@@ -1,4 +1,10 @@
-import { DeleteResult, Kysely, UpdateResult } from '..'
+import {
+  DeleteResult,
+  InsertResult,
+  Kysely,
+  UpdateResult,
+  expressionBuilder,
+} from '..'
 import { expectType } from 'tsd'
 
 async function testKyselyAnySelects(db: Kysely<any>) {
@@ -50,6 +56,34 @@ async function testKyselyAnySelects(db: Kysely<any>) {
   >(r5)
 }
 
+async function testKyselyAnyInserts(db: Kysely<any>) {
+  const r1 = await db
+    .insertInto('foo')
+    .values({ bar: 'baz', spam: 1 })
+    .executeTakeFirstOrThrow()
+  expectType<InsertResult>(r1)
+
+  const r2 = await db
+    .insertInto('foo')
+    .values({ bar: 'baz', spam: 1 })
+    .returning('foo')
+    .executeTakeFirstOrThrow()
+  expectType<{ foo: any }>(r2)
+
+  const r3 = await db
+    .insertInto('foo')
+    .values({ bar: 'baz', spam: 1 })
+    .returning(['foo', 'baz'])
+    .executeTakeFirstOrThrow()
+  expectType<{ foo: any; baz: any }>(r3)
+
+  const r4 = await db
+    .insertInto('foo')
+    .values((eb) => ({ foo: eb.ref('foo.bar') }))
+    .executeTakeFirstOrThrow()
+  expectType<InsertResult>(r4)
+}
+
 async function testKyselyAnyUpdates(db: Kysely<any>) {
   const r1 = await db
     .updateTable('foo')
@@ -74,6 +108,15 @@ async function testKyselyAnyUpdates(db: Kysely<any>) {
     .returning(['a', 'b'])
     .executeTakeFirstOrThrow()
   expectType<{ a: any; b: any }>(r3)
+
+  const r4 = await db
+    .updateTable('foo')
+    .set((eb) => ({
+      foo: eb('foo.bar', '=', 1),
+    }))
+    .where('foo.eggs', '=', 1)
+    .executeTakeFirstOrThrow()
+  expectType<UpdateResult>(r4)
 }
 
 async function testKyselyAnyDeletes(db: Kysely<any>) {