diff --git a/src/test-jdk17/java/com/fasterxml/jackson/databind/records/RecordCreatorWithAnySetter562Test.java b/src/test-jdk17/java/com/fasterxml/jackson/databind/records/RecordCreatorWithAnySetter562Test.java
index 9fee6af811..5bb2bf4393 100644
--- a/src/test-jdk17/java/com/fasterxml/jackson/databind/records/RecordCreatorWithAnySetter562Test.java
+++ b/src/test-jdk17/java/com/fasterxml/jackson/databind/records/RecordCreatorWithAnySetter562Test.java
@@ -7,30 +7,38 @@
 import com.fasterxml.jackson.databind.testutil.DatabindTestUtil;
 import org.junit.jupiter.api.Test;
 
+import java.util.LinkedHashMap;
 import java.util.Map;
 
 import static org.junit.jupiter.api.Assertions.assertEquals;
 
 // [databind#562] Allow @JsonAnySetter on Creator constructors
-public class RecordCreatorWithAnySetter562Test
-        extends DatabindTestUtil
+public class RecordCreatorWithAnySetter562Test extends DatabindTestUtil
 {
-    record RecordWithAnySetterCtor(int id,
-            Map<String, Integer> additionalProperties) {
+    record RecordWithAnySetterCtorParamCanonCtor(int id, Map<String, Integer> additionalProperties) {
         @JsonCreator
-        public RecordWithAnySetterCtor(@JsonProperty("regular") int id,
-                @JsonAnySetter Map<String, Integer> additionalProperties
-        ) {
+        public RecordWithAnySetterCtorParamCanonCtor(@JsonProperty("regular") int id,
+                                                     @JsonAnySetter Map<String, Integer> additionalProperties) {
             this.id = id;
             this.additionalProperties = additionalProperties;
         }
     }
 
-    /*
-    /**********************************************************************
-    /* Test methods, alternate constructors
-    /**********************************************************************
-     */
+    record RecordWithAnySetterComponentCanonCtor(int id, @JsonAnySetter Map<String, Object> any) {
+    }
+
+    // Workaround mentioned in [databind#3439]
+    record RecordWorkaroundWithAnySetterMethodWithAltCtor(int id, Map<String, Object> any) {
+        @JsonCreator
+        public RecordWorkaroundWithAnySetterMethodWithAltCtor(@JsonProperty("id") int id) {
+            this(id, new LinkedHashMap<>());
+        }
+
+        @JsonAnySetter
+        private void updateProperty(String name, Object value) {
+            any.put(name, value);
+        }
+    }
 
     private final ObjectMapper MAPPER = newJsonMapper();
 
@@ -38,17 +46,41 @@ public RecordWithAnySetterCtor(@JsonProperty("regular") int id,
     public void testRecordWithAnySetterCtor() throws Exception
     {
         // First, only regular property mapped
-        RecordWithAnySetterCtor result = MAPPER.readValue(a2q("{'regular':13}"),
-                RecordWithAnySetterCtor.class);
+        RecordWithAnySetterCtorParamCanonCtor result = MAPPER.readValue(a2q("{'regular':13}"),
+                RecordWithAnySetterCtorParamCanonCtor.class);
         assertEquals(13, result.id);
         assertEquals(0, result.additionalProperties.size());
 
         // Then with unknown properties
         result = MAPPER.readValue(a2q("{'regular':13, 'unknown':99, 'extra':-1}"),
-                RecordWithAnySetterCtor.class);
+                RecordWithAnySetterCtorParamCanonCtor.class);
         assertEquals(13, result.id);
         assertEquals(Integer.valueOf(99), result.additionalProperties.get("unknown"));
         assertEquals(Integer.valueOf(-1), result.additionalProperties.get("extra"));
         assertEquals(2, result.additionalProperties.size());
     }
+
+    @Test
+    public void testDeserialize_WithAnySetterComponent_WithCanonicalConstructor() throws Exception
+    {
+        RecordWithAnySetterComponentCanonCtor value = MAPPER.readValue(
+                a2q("{'id':123,'any1':'Any 1','any2':'Any 2'}"), RecordWithAnySetterComponentCanonCtor.class);
+
+        Map<String, Object> expectedAny = new LinkedHashMap<>();
+        expectedAny.put("any1", "Any 1");
+        expectedAny.put("any2", "Any 2");
+        assertEquals(new RecordWithAnySetterComponentCanonCtor(123, expectedAny), value);
+    }
+
+    @Test
+    public void testDeserializeWorkaround_WithAnySetterMethod_WithAltConstructor() throws Exception
+    {
+        RecordWorkaroundWithAnySetterMethodWithAltCtor value = MAPPER.readValue(
+                a2q("{'id':123,'any1':'Any 1','any2':'Any 2'}"), RecordWorkaroundWithAnySetterMethodWithAltCtor.class);
+
+        Map<String, Object> expectedAny = new LinkedHashMap<>();
+        expectedAny.put("any1", "Any 1");
+        expectedAny.put("any2", "Any 2");
+        assertEquals(new RecordWorkaroundWithAnySetterMethodWithAltCtor(123, expectedAny), value);
+    }
 }