diff --git a/idea/idea-fir/src/org/jetbrains/kotlin/idea/fir/intentions/HLConvertToBlockBodyIntention.kt b/idea/idea-fir/src/org/jetbrains/kotlin/idea/fir/intentions/HLConvertToBlockBodyIntention.kt
index a5e654a54cc..30c665b0cb9 100644
--- a/idea/idea-fir/src/org/jetbrains/kotlin/idea/fir/intentions/HLConvertToBlockBodyIntention.kt
+++ b/idea/idea-fir/src/org/jetbrains/kotlin/idea/fir/intentions/HLConvertToBlockBodyIntention.kt
@@ -36,7 +36,8 @@ class HLConvertToBlockBodyIntention :
         val reformat: Boolean,
     ) : HLApplicatorInput
 
-    override fun allowCaretInsideElement(element: PsiElement) = element !is KtDeclaration && super.allowCaretInsideElement(element)
+    override fun skipProcessingFurtherElementsAfter(element: PsiElement) =
+        element is KtDeclaration || super.skipProcessingFurtherElementsAfter(element)
 
     override val applicabilityRange: HLApplicabilityRange<KtDeclarationWithBody> get() = ApplicabilityRanges.SELF
 
diff --git a/idea/idea-frontend-independent/src/org/jetbrains/kotlin/idea/intentions/SelfTargetingIntention.kt b/idea/idea-frontend-independent/src/org/jetbrains/kotlin/idea/intentions/SelfTargetingIntention.kt
index f92ac860257..b06140bb3ab 100644
--- a/idea/idea-frontend-independent/src/org/jetbrains/kotlin/idea/intentions/SelfTargetingIntention.kt
+++ b/idea/idea-frontend-independent/src/org/jetbrains/kotlin/idea/intentions/SelfTargetingIntention.kt
@@ -79,7 +79,7 @@ abstract class SelfTargetingIntention<TElement : PsiElement>(
             if (elementType.isInstance(element) && isApplicableTo(element as TElement, offset)) {
                 return element
             }
-            if (element.textRange.containsInside(offset) && !allowCaretInsideElement(element)) break
+            if (element.textRange.containsInside(offset) && skipProcessingFurtherElementsAfter(element)) break
         }
         return null
     }
@@ -89,8 +89,16 @@ abstract class SelfTargetingIntention<TElement : PsiElement>(
         return getTarget(offset, file)
     }
 
-    /** Whether to keep looking for targets after having processed the given element, which contains the cursor. */
-    protected open fun allowCaretInsideElement(element: PsiElement): Boolean = element !is KtBlockExpression
+    /** Whether to keep looking for targets after having processed the given element, which contains the cursor.
+     * */
+    @Deprecated(
+        "The name of this method is a bit confusing and hence deprecated.",
+        replaceWith = ReplaceWith("!skipProcessingFurtherElementsAfter(element)")
+    )
+    protected open fun allowCaretInsideElement(element: PsiElement): Boolean = !skipProcessingFurtherElementsAfter(element)
+
+    /** Whether to skip looking for targets after having processed the given element, which contains the cursor. */
+    protected open fun skipProcessingFurtherElementsAfter(element: PsiElement): Boolean = element is KtBlockExpression
 
     final override fun isAvailable(project: Project, editor: Editor, file: PsiFile): Boolean {
         if (ApplicationManager.getApplication().isUnitTestMode) {
diff --git a/idea/src/org/jetbrains/kotlin/idea/inspections/FunctionWithLambdaExpressionBodyInspection.kt b/idea/src/org/jetbrains/kotlin/idea/inspections/FunctionWithLambdaExpressionBodyInspection.kt
index 6b79856c89f..4dc4a8b9861 100644
--- a/idea/src/org/jetbrains/kotlin/idea/inspections/FunctionWithLambdaExpressionBodyInspection.kt
+++ b/idea/src/org/jetbrains/kotlin/idea/inspections/FunctionWithLambdaExpressionBodyInspection.kt
@@ -68,7 +68,7 @@ class FunctionWithLambdaExpressionBodyInspection : AbstractKotlinInspection() {
     }
 
     private class AddArrowIntention : SpecifyExplicitLambdaSignatureIntention() {
-        override fun allowCaretInsideElement(element: PsiElement) = true
+        override fun skipProcessingFurtherElementsAfter(element: PsiElement): Boolean = false
     }
 
     private class RemoveBracesFix : LocalQuickFix {
diff --git a/idea/src/org/jetbrains/kotlin/idea/intentions/AddNameToArgumentIntention.kt b/idea/src/org/jetbrains/kotlin/idea/intentions/AddNameToArgumentIntention.kt
index aac71865519..f68bd369bf4 100644
--- a/idea/src/org/jetbrains/kotlin/idea/intentions/AddNameToArgumentIntention.kt
+++ b/idea/src/org/jetbrains/kotlin/idea/intentions/AddNameToArgumentIntention.kt
@@ -46,9 +46,9 @@ class AddNameToArgumentIntention : SelfTargetingIntention<KtValueArgument>(
         return true
     }
 
-    override fun allowCaretInsideElement(element: PsiElement) = element !is KtValueArgumentList &&
-            element !is KtContainerNode &&
-            super.allowCaretInsideElement(element)
+    override fun skipProcessingFurtherElementsAfter(element: PsiElement) = element is KtValueArgumentList ||
+            element is KtContainerNode ||
+            super.skipProcessingFurtherElementsAfter(element)
 
     override fun applyTo(element: KtValueArgument, editor: Editor?) {
         apply(element)
diff --git a/idea/src/org/jetbrains/kotlin/idea/intentions/ConvertPropertyInitializerToGetterIntention.kt b/idea/src/org/jetbrains/kotlin/idea/intentions/ConvertPropertyInitializerToGetterIntention.kt
index 8ece60bcd21..514c4e1d88b 100644
--- a/idea/src/org/jetbrains/kotlin/idea/intentions/ConvertPropertyInitializerToGetterIntention.kt
+++ b/idea/src/org/jetbrains/kotlin/idea/intentions/ConvertPropertyInitializerToGetterIntention.kt
@@ -33,9 +33,9 @@ class ConvertPropertyInitializerToGetterIntention : SelfTargetingRangeIntention<
             null
     }
 
-    override fun allowCaretInsideElement(element: PsiElement): Boolean {
+    override fun skipProcessingFurtherElementsAfter(element: PsiElement): Boolean {
         // do not work inside lambda's in initializer - they can be too big
-        return element !is KtDeclaration && super.allowCaretInsideElement(element)
+        return element is KtDeclaration || super.skipProcessingFurtherElementsAfter(element)
     }
 
     override fun applyTo(element: KtProperty, editor: Editor?) {
diff --git a/idea/src/org/jetbrains/kotlin/idea/intentions/ConvertToBlockBodyIntention.kt b/idea/src/org/jetbrains/kotlin/idea/intentions/ConvertToBlockBodyIntention.kt
index b12aa0e4948..c6195002b17 100644
--- a/idea/src/org/jetbrains/kotlin/idea/intentions/ConvertToBlockBodyIntention.kt
+++ b/idea/src/org/jetbrains/kotlin/idea/intentions/ConvertToBlockBodyIntention.kt
@@ -44,7 +44,8 @@ class ConvertToBlockBodyIntention : SelfTargetingIntention<KtDeclarationWithBody
         }
     }
 
-    override fun allowCaretInsideElement(element: PsiElement) = element !is KtDeclaration && super.allowCaretInsideElement(element)
+    override fun skipProcessingFurtherElementsAfter(element: PsiElement) =
+        element is KtDeclaration || super.skipProcessingFurtherElementsAfter(element)
 
     override fun applyTo(element: KtDeclarationWithBody, editor: Editor?) {
         convert(element, true)
diff --git a/idea/src/org/jetbrains/kotlin/idea/intentions/RemoveBracesIntention.kt b/idea/src/org/jetbrains/kotlin/idea/intentions/RemoveBracesIntention.kt
index 35024fde68b..dfb8fc73fbf 100644
--- a/idea/src/org/jetbrains/kotlin/idea/intentions/RemoveBracesIntention.kt
+++ b/idea/src/org/jetbrains/kotlin/idea/intentions/RemoveBracesIntention.kt
@@ -93,5 +93,5 @@ class RemoveBracesIntention : SelfTargetingIntention<KtElement>(KtElement::class
         }
     }
 
-    override fun allowCaretInsideElement(element: PsiElement) = element !is KtBlockExpression || element.parent is KtWhenEntry
+    override fun skipProcessingFurtherElementsAfter(element: PsiElement) = element is KtBlockExpression && element.parent !is KtWhenEntry
 }