diff --git a/Sources/CustomDump/Conformances/Swift.swift b/Sources/CustomDump/Conformances/Swift.swift
index a41477c..46ae214 100644
--- a/Sources/CustomDump/Conformances/Swift.swift
+++ b/Sources/CustomDump/Conformances/Swift.swift
@@ -7,6 +7,7 @@ extension Character: CustomDumpRepresentable {
 extension ObjectIdentifier: CustomDumpStringConvertible {
   public var customDumpDescription: String {
     self.debugDescription
+      .replacingOccurrences(of: "0x0*", with: "0x", options: .regularExpression)
   }
 }
 
diff --git a/Sources/CustomDump/Diff.swift b/Sources/CustomDump/Diff.swift
index 03def97..ee1bc2c 100644
--- a/Sources/CustomDump/Diff.swift
+++ b/Sources/CustomDump/Diff.swift
@@ -81,8 +81,17 @@ public func diff<T>(_ lhs: T, _ rhs: T, format: DiffFormat = .default) -> String
       areInIncreasingOrder: ((Mirror.Child, Mirror.Child) -> Bool)? = nil,
       _ transform: (inout Mirror.Child, Int) -> Void = { _, _ in }
     ) {
-      guard !lhsMirror.children.isEmpty || !rhsMirror.children.isEmpty
+      var lhsChildren = Array(lhsMirror.children)
+      var rhsChildren = Array(rhsMirror.children)
+
+      guard !isMirrorEqual(lhsChildren, rhsChildren)
       else {
+        print(
+          "// Not equal but no difference detected:"
+            .indenting(by: indent)
+            .indenting(with: format.both + " "),
+          to: &out
+        )
         print(
           _customDump(
             lhs,
@@ -142,9 +151,6 @@ public func diff<T>(_ lhs: T, _ rhs: T, format: DiffFormat = .default) -> String
         to: &out
       )
 
-      var lhsChildren = Array(lhsMirror.children)
-      var rhsChildren = Array(rhsMirror.children)
-
       if let areInIncreasingOrder = areInIncreasingOrder {
         lhsChildren.sort(by: areInIncreasingOrder)
         rhsChildren.sort(by: areInIncreasingOrder)
@@ -311,6 +317,14 @@ public func diff<T>(_ lhs: T, _ rhs: T, format: DiffFormat = .default) -> String
           to: &out
         )
       } else {
+        let showObjectIdentifiers = lhsItem != rhsItem
+          && isMirrorEqual(Array(lhsMirror.children), Array(rhsMirror.children))
+        let lhsMirror = showObjectIdentifiers
+          ? Mirror(lhs, children: [("_", lhsItem)] + lhsMirror.children, displayStyle: .class)
+          : lhsMirror
+        let rhsMirror = showObjectIdentifiers
+          ? Mirror(rhs, children: [("_", rhsItem)] + rhsMirror.children, displayStyle: .class)
+          : rhsMirror
         visitedItems.insert(lhsItem)
         diffChildren(
           lhsMirror,
diff --git a/Tests/CustomDumpTests/DiffTests.swift b/Tests/CustomDumpTests/DiffTests.swift
index 2d5057f..015a0f0 100644
--- a/Tests/CustomDumpTests/DiffTests.swift
+++ b/Tests/CustomDumpTests/DiffTests.swift
@@ -76,6 +76,28 @@ final class DiffTests: XCTestCase {
     )
   }
 
+  func testClassObjectIdentity() {
+    class User: NSObject {
+      let id = 42
+      let name = "Blob"
+    }
+
+    XCTAssertNoDifference(
+      diff(
+        User(),
+        User()
+      )?.replacingOccurrences(of: "0x[[:xdigit:]]+", with: "…", options: .regularExpression),
+      """
+        DiffTests.User(
+      -   _: ObjectIdentifier(…),
+      +   _: ObjectIdentifier(…),
+          id: 42,
+          name: "Blob"
+        )
+      """
+    )
+  }
+
   func testCollection() {
     XCTAssertNoDifference(
       diff(
@@ -357,6 +379,7 @@ final class DiffTests: XCTestCase {
         NeverEqual()
       ),
       """
+        // Not equal but no difference detected:
       - NeverEqual()
       + NeverEqual()
       """
@@ -416,6 +439,18 @@ final class DiffTests: XCTestCase {
         )
       """
     )
+
+    XCTAssertNoDifference(
+      diff(
+        NeverEqualUser(id: 1, name: "Blob"),
+        NeverEqualUser(id: 1, name: "Blob")
+      ),
+      """
+        // Not equal but no difference detected:
+      - NeverEqualUser(…)
+      + NeverEqualUser(…)
+      """
+    )
   }
 
   func testTuple() {
diff --git a/Tests/CustomDumpTests/Mocks.swift b/Tests/CustomDumpTests/Mocks.swift
index f33e92c..b8a36a7 100644
--- a/Tests/CustomDumpTests/Mocks.swift
+++ b/Tests/CustomDumpTests/Mocks.swift
@@ -82,6 +82,13 @@ struct NestedDate { var date: Date? }
 
 struct NeverEqual: Equatable { static func == (lhs: Self, rhs: Self) -> Bool { false } }
 
+struct NeverEqualUser: Equatable {
+  let id: Int
+  let name: String
+
+  static func == (lhs: Self, rhs: Self) -> Bool { false }
+}
+
 struct Pair { let driver: User, passenger: User }
 
 struct Redacted<RawValue>: CustomDumpStringConvertible {