diff --git a/compiler/fir/fir2ir/tests-gen/org/jetbrains/kotlin/test/runners/codegen/FirLightTreeBlackBoxCodegenTestGenerated.java b/compiler/fir/fir2ir/tests-gen/org/jetbrains/kotlin/test/runners/codegen/FirLightTreeBlackBoxCodegenTestGenerated.java
index 6fe5fc177d0..69330b2221f 100644
--- a/compiler/fir/fir2ir/tests-gen/org/jetbrains/kotlin/test/runners/codegen/FirLightTreeBlackBoxCodegenTestGenerated.java
+++ b/compiler/fir/fir2ir/tests-gen/org/jetbrains/kotlin/test/runners/codegen/FirLightTreeBlackBoxCodegenTestGenerated.java
@@ -18671,6 +18671,12 @@ public class FirLightTreeBlackBoxCodegenTestGenerated extends AbstractFirLightTr
             runTest("compiler/testData/codegen/box/fir/syntheticPropertyThroughJavaMultiModule.kt");
         }
 
+        @Test
+        @TestMetadata("syntheticPropertyThroughJavaWithSetter.kt")
+        public void testSyntheticPropertyThroughJavaWithSetter() throws Exception {
+            runTest("compiler/testData/codegen/box/fir/syntheticPropertyThroughJavaWithSetter.kt");
+        }
+
         @Test
         @TestMetadata("toLong.kt")
         public void testToLong() throws Exception {
diff --git a/compiler/fir/fir2ir/tests-gen/org/jetbrains/kotlin/test/runners/codegen/FirPsiBlackBoxCodegenTestGenerated.java b/compiler/fir/fir2ir/tests-gen/org/jetbrains/kotlin/test/runners/codegen/FirPsiBlackBoxCodegenTestGenerated.java
index 45047f16b39..2f0700752a4 100644
--- a/compiler/fir/fir2ir/tests-gen/org/jetbrains/kotlin/test/runners/codegen/FirPsiBlackBoxCodegenTestGenerated.java
+++ b/compiler/fir/fir2ir/tests-gen/org/jetbrains/kotlin/test/runners/codegen/FirPsiBlackBoxCodegenTestGenerated.java
@@ -18671,6 +18671,12 @@ public class FirPsiBlackBoxCodegenTestGenerated extends AbstractFirPsiBlackBoxCo
             runTest("compiler/testData/codegen/box/fir/syntheticPropertyThroughJavaMultiModule.kt");
         }
 
+        @Test
+        @TestMetadata("syntheticPropertyThroughJavaWithSetter.kt")
+        public void testSyntheticPropertyThroughJavaWithSetter() throws Exception {
+            runTest("compiler/testData/codegen/box/fir/syntheticPropertyThroughJavaWithSetter.kt");
+        }
+
         @Test
         @TestMetadata("toLong.kt")
         public void testToLong() throws Exception {
diff --git a/compiler/fir/java/src/org/jetbrains/kotlin/fir/java/scopes/JavaClassUseSiteMemberScope.kt b/compiler/fir/java/src/org/jetbrains/kotlin/fir/java/scopes/JavaClassUseSiteMemberScope.kt
index f2e3c508a66..0584244441c 100644
--- a/compiler/fir/java/src/org/jetbrains/kotlin/fir/java/scopes/JavaClassUseSiteMemberScope.kt
+++ b/compiler/fir/java/src/org/jetbrains/kotlin/fir/java/scopes/JavaClassUseSiteMemberScope.kt
@@ -196,7 +196,7 @@ class JavaClassUseSiteMemberScope(
 
             candidateSymbol.takeIf {
                 when {
-                    candidate.isJavaOrEnhancement ->
+                    candidate.isAcceptableAsAccessorOverride() ->
                         // TODO: Decide something for the case when property type is not computed yet
                         expectedReturnType == null ||
                                 AbstractTypeChecker.isSubtypeOf(session.typeContext, candidateReturnType, expectedReturnType)
@@ -220,11 +220,20 @@ class JavaClassUseSiteMemberScope(
                 candidate.valueParameters.single().returnTypeRef.toConeKotlinTypeProbablyFlexible(session, typeParameterStack)
 
             candidateSymbol.takeIf {
-                candidate.isJavaOrEnhancement && AbstractTypeChecker.equalTypes(session.typeContext, parameterType, propertyType)
+                candidate.isAcceptableAsAccessorOverride() && AbstractTypeChecker.equalTypes(
+                    session.typeContext, parameterType, propertyType
+                )
             }
         }
     }
 
+    private fun FirSimpleFunction.isAcceptableAsAccessorOverride(): Boolean {
+        // We don't accept here accessors with type parameters from Kotlin to avoid strange cases like KT-59038
+        // However, we (temporarily, see below) accept accessors from Kotlin in general to keep K1 compatibility in cases like KT-59550
+        // KT-59601: we are going to forbid accessors from Kotlin in general after some investigation and/or deprecation period
+        return isJavaOrEnhancement || typeParameters.isEmpty()
+    }
+
     private fun FirPropertySymbol.getBuiltinSpecialPropertyGetterName(): Name? {
         var result: Name? = null
         superTypeScopes.processOverriddenPropertiesAndSelf(this) { overridden ->
diff --git a/compiler/testData/codegen/box/fir/syntheticPropertyThroughJava.kt b/compiler/testData/codegen/box/fir/syntheticPropertyThroughJava.kt
index 6bf489e4758..17b129ceb85 100644
--- a/compiler/testData/codegen/box/fir/syntheticPropertyThroughJava.kt
+++ b/compiler/testData/codegen/box/fir/syntheticPropertyThroughJava.kt
@@ -1,5 +1,4 @@
 // TARGET_BACKEND: JVM_IR
-// IGNORE_BACKEND_K2: JVM_IR
 // ISSUE: KT-59550
 
 // FILE: Intermediate.java
diff --git a/compiler/testData/codegen/box/fir/syntheticPropertyThroughJavaWithSetter.kt b/compiler/testData/codegen/box/fir/syntheticPropertyThroughJavaWithSetter.kt
new file mode 100644
index 00000000000..4e6e0b0bc0d
--- /dev/null
+++ b/compiler/testData/codegen/box/fir/syntheticPropertyThroughJavaWithSetter.kt
@@ -0,0 +1,26 @@
+// TARGET_BACKEND: JVM_IR
+// ISSUE: KT-59550
+
+// FILE: Intermediate.java
+public class Intermediate extends Base {
+    public Intermediate(String foo) {
+        super(foo);
+    }
+}
+
+// FILE: FinalAndBase.kt
+abstract class Base(private var foo: String) {
+    fun getFoo() = foo
+
+    fun setFoo(newFoo: String) {
+        foo = newFoo
+    }
+}
+
+class Final(val i: Intermediate) : Intermediate(i.foo)
+
+fun box(): String {
+    val f = Final(Intermediate(""))
+    f.foo = "OK"
+    return f.foo
+}
diff --git a/compiler/tests-common-new/tests-gen/org/jetbrains/kotlin/test/runners/codegen/IrBlackBoxCodegenTestGenerated.java b/compiler/tests-common-new/tests-gen/org/jetbrains/kotlin/test/runners/codegen/IrBlackBoxCodegenTestGenerated.java
index 92188d857f0..f8a1d95f0c3 100644
--- a/compiler/tests-common-new/tests-gen/org/jetbrains/kotlin/test/runners/codegen/IrBlackBoxCodegenTestGenerated.java
+++ b/compiler/tests-common-new/tests-gen/org/jetbrains/kotlin/test/runners/codegen/IrBlackBoxCodegenTestGenerated.java
@@ -18671,6 +18671,12 @@ public class IrBlackBoxCodegenTestGenerated extends AbstractIrBlackBoxCodegenTes
             runTest("compiler/testData/codegen/box/fir/syntheticPropertyThroughJavaMultiModule.kt");
         }
 
+        @Test
+        @TestMetadata("syntheticPropertyThroughJavaWithSetter.kt")
+        public void testSyntheticPropertyThroughJavaWithSetter() throws Exception {
+            runTest("compiler/testData/codegen/box/fir/syntheticPropertyThroughJavaWithSetter.kt");
+        }
+
         @Test
         @TestMetadata("toLong.kt")
         public void testToLong() throws Exception {
diff --git a/compiler/tests-common-new/tests-gen/org/jetbrains/kotlin/test/runners/codegen/IrBlackBoxCodegenWithIrInlinerTestGenerated.java b/compiler/tests-common-new/tests-gen/org/jetbrains/kotlin/test/runners/codegen/IrBlackBoxCodegenWithIrInlinerTestGenerated.java
index 1ba803ac766..b4656320aef 100644
--- a/compiler/tests-common-new/tests-gen/org/jetbrains/kotlin/test/runners/codegen/IrBlackBoxCodegenWithIrInlinerTestGenerated.java
+++ b/compiler/tests-common-new/tests-gen/org/jetbrains/kotlin/test/runners/codegen/IrBlackBoxCodegenWithIrInlinerTestGenerated.java
@@ -18671,6 +18671,12 @@ public class IrBlackBoxCodegenWithIrInlinerTestGenerated extends AbstractIrBlack
             runTest("compiler/testData/codegen/box/fir/syntheticPropertyThroughJavaMultiModule.kt");
         }
 
+        @Test
+        @TestMetadata("syntheticPropertyThroughJavaWithSetter.kt")
+        public void testSyntheticPropertyThroughJavaWithSetter() throws Exception {
+            runTest("compiler/testData/codegen/box/fir/syntheticPropertyThroughJavaWithSetter.kt");
+        }
+
         @Test
         @TestMetadata("toLong.kt")
         public void testToLong() throws Exception {