diff --git a/src/diff/children.js b/src/diff/children.js
index ba2730478c..84d550e8ae 100644
--- a/src/diff/children.js
+++ b/src/diff/children.js
@@ -398,8 +398,9 @@ function findMatchingIndex(
 	// if the oldVNode was null or matched, then there could needs to be at least
 	// 1 (aka `remainingOldChildren > 0`) children to find and compare against.
 	let shouldSearch =
+		(typeof type !== 'function' || type === Fragment || key) &&
 		remainingOldChildren >
-		(oldVNode != null && (oldVNode._flags & MATCHED) === 0 ? 1 : 0);
+			(oldVNode != null && (oldVNode._flags & MATCHED) === 0 ? 1 : 0);
 
 	if (
 		oldVNode === null ||
diff --git a/test/browser/render.test.js b/test/browser/render.test.js
index 96bef10bb0..39b0ad86ba 100644
--- a/test/browser/render.test.js
+++ b/test/browser/render.test.js
@@ -1786,6 +1786,37 @@ describe('render()', () => {
 		);
 	});
 
+	// #2949
+	it('should not swap unkeyed chlildren', () => {
+		class X extends Component {
+			constructor(props) {
+				super(props);
+				this.name = props.name;
+			}
+			render() {
+				return <p>{this.name}</p>;
+			}
+		}
+
+		function Foo({ condition }) {
+			return (
+				<div>
+					{condition ? '' : <X name="A" />}
+					{condition ? <X name="B" /> : ''}
+				</div>
+			);
+		}
+
+		render(<Foo />, scratch);
+		expect(scratch.textContent).to.equal('A');
+
+		render(<Foo condition />, scratch);
+		expect(scratch.textContent).to.equal('B');
+
+		render(<Foo />, scratch);
+		expect(scratch.textContent).to.equal('A');
+	});
+
 	it('handle shuffled (stress test)', () => {
 		function randomize(arr) {
 			for (let i = arr.length - 1; i > 0; i--) {