diff --git a/compiler/resolution.common/src/org/jetbrains/kotlin/resolve/calls/inference/components/VariableFixationFinder.kt b/compiler/resolution.common/src/org/jetbrains/kotlin/resolve/calls/inference/components/VariableFixationFinder.kt
index 27ec88c4f39..91bb087104c 100644
--- a/compiler/resolution.common/src/org/jetbrains/kotlin/resolve/calls/inference/components/VariableFixationFinder.kt
+++ b/compiler/resolution.common/src/org/jetbrains/kotlin/resolve/calls/inference/components/VariableFixationFinder.kt
@@ -141,8 +141,12 @@ class VariableFixationFinder(
         return false
     }
 
-    private fun Context.variableHasProperArgumentConstraints(variable: TypeConstructorMarker): Boolean =
-        notFixedTypeVariables[variable]?.constraints?.any { isProperArgumentConstraint(it) } ?: false
+    private fun Context.variableHasProperArgumentConstraints(variable: TypeConstructorMarker): Boolean {
+        val constraints = notFixedTypeVariables[variable]?.constraints ?: return false
+        // temporary hack to fail calls which contain callable references resolved though OI with uninferred type parameters
+        val areThereConstraintsWithUninferredTypeParameter = constraints.any { c -> c.type.contains { it.isUninferredParameter() } }
+        return constraints.any { isProperArgumentConstraint(it) } && !areThereConstraintsWithUninferredTypeParameter
+    }
 
     private fun Context.isProperArgumentConstraint(c: Constraint) =
         isProperType(c.type)
@@ -167,7 +171,7 @@ inline fun TypeSystemInferenceExtensionContext.isProperTypeForFixation(
     type: KotlinTypeMarker,
     isProper: (KotlinTypeMarker) -> Boolean
 ): Boolean {
-    if (!isProper(type) || type.contains { it.isUninferredParameter() }) return false
+    if (!isProper(type)) return false
     if (type.isCapturedType()) {
         val projection = (type as? SimpleTypeMarker)?.asCapturedType()?.typeConstructorProjection() ?: return true
         if (projection.isStarProjection()) return true
diff --git a/compiler/testData/codegen/box/inference/builderInference/specialCallsWithLambdas.kt b/compiler/testData/codegen/box/inference/builderInference/specialCallsWithLambdas.kt
index c9a7f6ff984..831e28658cc 100644
--- a/compiler/testData/codegen/box/inference/builderInference/specialCallsWithLambdas.kt
+++ b/compiler/testData/codegen/box/inference/builderInference/specialCallsWithLambdas.kt
@@ -1,4 +1,5 @@
 // WITH_RUNTIME
+// IGNORE_BACKEND_FIR: JVM_IR
 
 import kotlin.experimental.ExperimentalTypeInference
 
diff --git a/compiler/testData/codegen/box/inference/specialCallsWithCallableReferences.kt b/compiler/testData/codegen/box/inference/specialCallsWithCallableReferences.kt
index be48cfab68d..56b57fa7ce8 100644
--- a/compiler/testData/codegen/box/inference/specialCallsWithCallableReferences.kt
+++ b/compiler/testData/codegen/box/inference/specialCallsWithCallableReferences.kt
@@ -32,12 +32,6 @@ fun poll16(flag: Boolean): Any? {
     return inv()
 }
 
-// TODO
-//fun poll17(flag: Boolean): Any? {
-//    val inv = if (flag) { foo7() } else { ::Foo7 }
-//    return inv
-//}
-
 fun poll21(flag: Boolean): Any? {
     val inv = when (flag) { true -> ::bar2 else -> ::foo2 }
     return inv()
@@ -48,12 +42,6 @@ fun poll25(flag: Boolean): Any? {
     return inv
 }
 
-// TODO
-//fun poll26(flag: Boolean): Any? {
-//    val inv = when (flag) { true -> ::Foo7 false -> foo7() else -> ::Foo7 }
-//    return inv
-//}
-
 fun poll31(flag: Boolean): Any? {
     val inv = when (flag) { true -> ::bar2 false -> ::foo2 }
     return inv()
@@ -64,12 +52,6 @@ fun poll35(flag: Boolean): Any? {
     return inv
 }
 
-// TODO
-//fun poll36(flag: Boolean): Any? {
-//    val inv = when (flag) { true -> ::Foo7 false -> foo7() }
-//    return inv
-//}
-
 fun poll41(): Any? {
     val inv = try { ::bar2 } finally { ::foo2 }
     return inv()
@@ -90,12 +72,6 @@ fun poll55(): Any? {
     return inv()
 }
 
-// TODO
-//fun poll56(): Any? {
-//    val inv = try { ::Foo7 } catch (e: Exception) { foo7() } finally { foo7() }
-//    return inv
-//}
-
 fun poll61(): Any? {
     val inv = ::bar2
     return inv
@@ -121,7 +97,6 @@ fun poll81(): Any? {
     return inv
 }
 
-
 fun poll85(): Any? {
     val inv = ::Foo6 in setOf(::Foo6)
     return inv
@@ -131,18 +106,14 @@ fun box(): String {
     poll1(true)
     poll11(true)
     poll16(true)
-//    poll17(true)
     poll21(true)
     poll25(true)
-//    poll26(true)
     poll31(true)
     poll35(true)
-//    poll36(true)
     poll41()
     poll45()
     poll51()
     poll55()
-//    poll56()
     poll61()
     poll65()
     poll71()
diff --git a/compiler/testData/diagnostics/tests/inference/builderInference/specialCallsWithCallableReferences.kt b/compiler/testData/diagnostics/tests/inference/builderInference/specialCallsWithCallableReferences.kt
index 1bf84cc30a8..ad9b44a3dc4 100644
--- a/compiler/testData/diagnostics/tests/inference/builderInference/specialCallsWithCallableReferences.kt
+++ b/compiler/testData/diagnostics/tests/inference/builderInference/specialCallsWithCallableReferences.kt
@@ -136,8 +136,8 @@ fun poll16(flag: Boolean): Flow<String> {
 
 fun poll17(flag: Boolean): Flow<String> {
     return flow {
-        val inv = if (flag) { <!IMPLICIT_CAST_TO_ANY!>foo7()<!> } else { <!IMPLICIT_CAST_TO_ANY!>::Foo7<!> }
-        inv
+        val inv = if (flag) { foo7() } else { <!NEW_INFERENCE_NO_INFORMATION_FOR_PARAMETER!>::Foo7<!> }
+        <!DEBUG_INFO_ELEMENT_WITH_ERROR_TYPE!>inv<!>
     }
 }
 
@@ -185,7 +185,7 @@ fun poll25(flag: Boolean): Flow<String> {
 
 fun poll26(flag: Boolean): Flow<String> {
     return flow {
-        val inv = when (flag) { true -> <!IMPLICIT_CAST_TO_ANY!>::Foo7<!> false -> <!IMPLICIT_CAST_TO_ANY!>foo7()<!> <!REDUNDANT_ELSE_IN_WHEN!>else<!> -> <!IMPLICIT_CAST_TO_ANY!>::Foo7<!> }
+        val inv = when (flag) { true -> <!IMPLICIT_CAST_TO_ANY, NEW_INFERENCE_NO_INFORMATION_FOR_PARAMETER!>::Foo7<!> false -> <!IMPLICIT_CAST_TO_ANY!>foo7()<!> <!REDUNDANT_ELSE_IN_WHEN!>else<!> -> <!IMPLICIT_CAST_TO_ANY, NEW_INFERENCE_NO_INFORMATION_FOR_PARAMETER!>::Foo7<!> }
         inv
     }
 }
@@ -234,7 +234,7 @@ fun poll35(flag: Boolean): Flow<String> {
 
 fun poll36(flag: Boolean): Flow<String> {
     return flow {
-        val inv = when (flag) { true -> <!IMPLICIT_CAST_TO_ANY!>::Foo7<!> false -> <!IMPLICIT_CAST_TO_ANY!>foo7()<!> }
+        val inv = when (flag) { true -> <!IMPLICIT_CAST_TO_ANY, NEW_INFERENCE_NO_INFORMATION_FOR_PARAMETER!>::Foo7<!> false -> <!IMPLICIT_CAST_TO_ANY!>foo7()<!> }
         inv
     }
 }
@@ -332,8 +332,8 @@ fun poll55(): Flow<String> {
 
 fun poll56(): Flow<String> {
     return flow {
-        val inv = try { ::Foo7 } catch (e: Exception) { foo7() } finally { foo7() }
-        inv
+        val inv = try { <!NEW_INFERENCE_NO_INFORMATION_FOR_PARAMETER!>::Foo7<!> } catch (e: Exception) { foo7() } finally { foo7() }
+        <!DEBUG_INFO_ELEMENT_WITH_ERROR_TYPE!>inv<!>
     }
 }
 
diff --git a/compiler/testData/diagnostics/tests/inference/builderInference/specialCallsWithCallableReferencesDontCareTypeInBlockExression.kt b/compiler/testData/diagnostics/tests/inference/builderInference/specialCallsWithCallableReferencesDontCareTypeInBlockExression.kt
index e87e69c10a7..fbf0f6f9699 100644
--- a/compiler/testData/diagnostics/tests/inference/builderInference/specialCallsWithCallableReferencesDontCareTypeInBlockExression.kt
+++ b/compiler/testData/diagnostics/tests/inference/builderInference/specialCallsWithCallableReferencesDontCareTypeInBlockExression.kt
@@ -85,8 +85,8 @@ fun poll16(flag: Boolean): Flow<String> {
 
 fun poll17(flag: Boolean): Flow<String> {
     return flow {
-        val inv = if (flag) { <!IMPLICIT_CAST_TO_ANY!>foo7()<!> } else { <!IMPLICIT_CAST_TO_ANY!>::Foo7<!> }
-        inv
+        val inv = if (flag) { foo7() } else { <!NEW_INFERENCE_NO_INFORMATION_FOR_PARAMETER!>::Foo7<!> }
+        <!DEBUG_INFO_ELEMENT_WITH_ERROR_TYPE!>inv<!>
     }
 }
 
@@ -183,7 +183,7 @@ fun poll55(): Flow<String> {
 
 fun poll56(): Flow<String> {
     return flow {
-        val inv = try { ::Foo7 } catch (e: Exception) { foo7() } finally { foo7() }
-        inv
+        val inv = try { <!NEW_INFERENCE_NO_INFORMATION_FOR_PARAMETER!>::Foo7<!> } catch (e: Exception) { foo7() } finally { foo7() }
+        <!DEBUG_INFO_ELEMENT_WITH_ERROR_TYPE!>inv<!>
     }
 }
diff --git a/compiler/testData/diagnostics/tests/inference/reportNotEnoughTypeInformationErrorsOnBlockExpressions.kt b/compiler/testData/diagnostics/tests/inference/reportNotEnoughTypeInformationErrorsOnBlockExpressions.kt
index d98af6dcace..7db303c5969 100644
--- a/compiler/testData/diagnostics/tests/inference/reportNotEnoughTypeInformationErrorsOnBlockExpressions.kt
+++ b/compiler/testData/diagnostics/tests/inference/reportNotEnoughTypeInformationErrorsOnBlockExpressions.kt
@@ -9,8 +9,8 @@ class Foo7<T>
 fun foo7() = null as Foo7<Int>
 
 fun poll17(flag: Boolean): Any? {
-    val inv = if (flag) { <!IMPLICIT_CAST_TO_ANY!>foo7()<!> } else { <!IMPLICIT_CAST_TO_ANY!>::Foo7<!> }
-    return inv
+    val inv = if (flag) { foo7() } else { <!NEW_INFERENCE_NO_INFORMATION_FOR_PARAMETER!>::Foo7<!> }
+    return <!DEBUG_INFO_ELEMENT_WITH_ERROR_TYPE!>inv<!>
 }
 
 fun poll26(flag: Boolean): Any? {
@@ -24,6 +24,6 @@ fun poll36(flag: Boolean): Any? {
 }
 
 fun poll56(): Any? {
-    val inv = try { ::Foo7 } catch (e: Exception) { foo7() } finally { foo7() }
-    return inv
+    val inv = try { <!NEW_INFERENCE_NO_INFORMATION_FOR_PARAMETER!>::Foo7<!> } catch (e: Exception) { foo7() } finally { foo7() }
+    return <!DEBUG_INFO_ELEMENT_WITH_ERROR_TYPE!>inv<!>
 }
diff --git a/compiler/testData/diagnostics/tests/inference/reportingImprovements/kt42620.kt b/compiler/testData/diagnostics/tests/inference/reportingImprovements/kt42620.kt
index 66cd0c6cbae..04b2d5c3703 100644
--- a/compiler/testData/diagnostics/tests/inference/reportingImprovements/kt42620.kt
+++ b/compiler/testData/diagnostics/tests/inference/reportingImprovements/kt42620.kt
@@ -3,10 +3,10 @@
 class Foo
 
 fun main1() = when {
-    else -> <!TYPE_MISMATCH!>Foo::plus<!>
+    else -> <!NEW_INFERENCE_NO_INFORMATION_FOR_PARAMETER, TYPE_MISMATCH!>Foo::plus<!>
 }
 
-fun main2() = if (true) Foo::<!UNRESOLVED_REFERENCE!>minus<!> else Foo::<!UNRESOLVED_REFERENCE!>times<!>
+fun main2() = if (true) <!NEW_INFERENCE_NO_INFORMATION_FOR_PARAMETER!>Foo::<!UNRESOLVED_REFERENCE!>minus<!><!> else <!NEW_INFERENCE_NO_INFORMATION_FOR_PARAMETER!>Foo::<!UNRESOLVED_REFERENCE!>times<!><!>
 
 fun main3() = if (true) { Foo::<!UNRESOLVED_REFERENCE!>minus<!> } else { Foo::<!UNRESOLVED_REFERENCE!>times<!> }
 
diff --git a/compiler/testData/diagnostics/tests/inference/specialCallsWithCallableReferences.kt b/compiler/testData/diagnostics/tests/inference/specialCallsWithCallableReferences.kt
index dc153a98e5b..2ee1eebab8f 100644
--- a/compiler/testData/diagnostics/tests/inference/specialCallsWithCallableReferences.kt
+++ b/compiler/testData/diagnostics/tests/inference/specialCallsWithCallableReferences.kt
@@ -54,8 +54,8 @@ fun poll16(flag: Boolean) {
 }
 
 fun poll17(flag: Boolean) {
-    val inv = if (flag) { <!IMPLICIT_CAST_TO_ANY!>foo7()<!> } else { <!IMPLICIT_CAST_TO_ANY!>::Foo7<!> }
-    inv
+    val inv = if (flag) { foo7() } else { <!NEW_INFERENCE_NO_INFORMATION_FOR_PARAMETER!>::Foo7<!> }
+    <!DEBUG_INFO_ELEMENT_WITH_ERROR_TYPE!>inv<!>
 }
 
 fun poll2(flag: Boolean) {
@@ -89,7 +89,7 @@ fun poll25(flag: Boolean) {
 }
 
 fun poll26(flag: Boolean) {
-    val inv = when (flag) { true -> <!IMPLICIT_CAST_TO_ANY!>::Foo7<!> false -> <!IMPLICIT_CAST_TO_ANY!>foo7()<!> <!REDUNDANT_ELSE_IN_WHEN!>else<!> -> <!IMPLICIT_CAST_TO_ANY!>::Foo7<!> }
+    val inv = when (flag) { true -> <!IMPLICIT_CAST_TO_ANY, NEW_INFERENCE_NO_INFORMATION_FOR_PARAMETER!>::Foo7<!> false -> <!IMPLICIT_CAST_TO_ANY!>foo7()<!> <!REDUNDANT_ELSE_IN_WHEN!>else<!> -> <!IMPLICIT_CAST_TO_ANY, NEW_INFERENCE_NO_INFORMATION_FOR_PARAMETER!>::Foo7<!> }
     inv
 }
 
@@ -124,7 +124,7 @@ fun poll35(flag: Boolean) {
 }
 
 fun poll36(flag: Boolean) {
-    val inv = when (flag) { true -> <!IMPLICIT_CAST_TO_ANY!>::Foo7<!> false -> <!IMPLICIT_CAST_TO_ANY!>foo7()<!> }
+    val inv = when (flag) { true -> <!IMPLICIT_CAST_TO_ANY, NEW_INFERENCE_NO_INFORMATION_FOR_PARAMETER!>::Foo7<!> false -> <!IMPLICIT_CAST_TO_ANY!>foo7()<!> }
     inv
 }
 
@@ -194,8 +194,8 @@ fun poll55() {
 }
 
 fun poll56() {
-    val inv = try { ::Foo7 } catch (e: Exception) { foo7() } finally { foo7() }
-    inv
+    val inv = try { <!NEW_INFERENCE_NO_INFORMATION_FOR_PARAMETER!>::Foo7<!> } catch (e: Exception) { foo7() } finally { foo7() }
+    <!DEBUG_INFO_ELEMENT_WITH_ERROR_TYPE!>inv<!>
 }
 
 fun poll6() {