diff --git a/idea/idea-fir/src/org/jetbrains/kotlin/idea/fir/api/AbstractHLIntention.kt b/idea/idea-fir/src/org/jetbrains/kotlin/idea/fir/api/AbstractHLIntention.kt
index 901d22bffaa..1c75d41ef05 100644
--- a/idea/idea-fir/src/org/jetbrains/kotlin/idea/fir/api/AbstractHLIntention.kt
+++ b/idea/idea-fir/src/org/jetbrains/kotlin/idea/fir/api/AbstractHLIntention.kt
@@ -26,6 +26,11 @@ abstract class AbstractHLIntention<PSI : KtElement, INPUT : HLApplicatorInput>(
         if (!applicator.isApplicableByPsi(element, project)) return false
         val ranges = applicabilityRange.getApplicabilityRanges(element)
         if (ranges.isEmpty()) return false
+
+        // An HLApplicabilityRange should be relative to the element, while `caretOffset` is absolute
+        val relativeCaretOffset = caretOffset - element.textRange.startOffset
+        if (ranges.none { it.containsOffset(relativeCaretOffset) }) return false
+
         val input = getInput(element)
         if (input != null && input.isValidFor(element)) {
             setFamilyNameGetter(applicator::getFamilyName)
diff --git a/idea/idea-fir/src/org/jetbrains/kotlin/idea/fir/intentions/HLAddAccessorIntentions.kt b/idea/idea-fir/src/org/jetbrains/kotlin/idea/fir/intentions/HLAddAccessorIntentions.kt
index 3527e7950af..56c4ad03304 100644
--- a/idea/idea-fir/src/org/jetbrains/kotlin/idea/fir/intentions/HLAddAccessorIntentions.kt
+++ b/idea/idea-fir/src/org/jetbrains/kotlin/idea/fir/intentions/HLAddAccessorIntentions.kt
@@ -12,8 +12,8 @@ import org.jetbrains.kotlin.idea.api.applicator.applicator
 import org.jetbrains.kotlin.idea.fir.api.AbstractHLIntention
 import org.jetbrains.kotlin.idea.fir.api.applicator.HLApplicabilityRange
 import org.jetbrains.kotlin.idea.fir.api.applicator.HLApplicatorInputProvider
+import org.jetbrains.kotlin.idea.fir.api.applicator.applicabilityTarget
 import org.jetbrains.kotlin.idea.fir.api.applicator.inputProvider
-import org.jetbrains.kotlin.idea.fir.applicators.ApplicabilityRanges
 import org.jetbrains.kotlin.idea.frontend.api.symbols.KtPropertySymbol
 import org.jetbrains.kotlin.idea.intentions.AbstractAddAccessorsIntention
 import org.jetbrains.kotlin.lexer.KtTokens
@@ -26,8 +26,9 @@ import org.jetbrains.kotlin.psi.psiUtil.hasExpectModifier
 
 abstract class HLAddAccessorIntention(private val addGetter: Boolean, private val addSetter: Boolean) :
     AbstractHLIntention<KtProperty, HLApplicatorInput.Empty>(KtProperty::class) {
-    // TODO: Copy and test range from AddAccessorIntentions.applicabilityRange
-    override val applicabilityRange: HLApplicabilityRange<KtProperty> = ApplicabilityRanges.SELF
+    override val applicabilityRange: HLApplicabilityRange<KtProperty> = applicabilityTarget { ktProperty ->
+        if (ktProperty.hasInitializer()) ktProperty.nameIdentifier else ktProperty
+    }
 
     override val applicator: HLApplicator<KtProperty, HLApplicatorInput.Empty> = applicator {
         applyTo { ktProperty, _, _, editor ->
diff --git a/idea/idea-fir/tests/org/jetbrains/kotlin/idea/fir/intentions/HLIntentionTestGenerated.java b/idea/idea-fir/tests/org/jetbrains/kotlin/idea/fir/intentions/HLIntentionTestGenerated.java
index d936abb89ff..5bb6ad55ee2 100644
--- a/idea/idea-fir/tests/org/jetbrains/kotlin/idea/fir/intentions/HLIntentionTestGenerated.java
+++ b/idea/idea-fir/tests/org/jetbrains/kotlin/idea/fir/intentions/HLIntentionTestGenerated.java
@@ -48,6 +48,11 @@ public class HLIntentionTestGenerated extends AbstractHLIntentionTest {
                 KtTestUtil.assertAllTestsPresentByMetadataWithExcluded(this.getClass(), new File("idea/testData/intentions/addPropertyAccessors/both"), Pattern.compile("^([\\w\\-_]+)\\.(kt|kts)$"), null, true);
             }
 
+            @TestMetadata("caretNotOnName.kt")
+            public void testCaretNotOnName() throws Exception {
+                runTest("idea/testData/intentions/addPropertyAccessors/both/caretNotOnName.kt");
+            }
+
             @TestMetadata("delegate.kt")
             public void testDelegate() throws Exception {
                 runTest("idea/testData/intentions/addPropertyAccessors/both/delegate.kt");
@@ -126,6 +131,11 @@ public class HLIntentionTestGenerated extends AbstractHLIntentionTest {
                 KtTestUtil.assertAllTestsPresentByMetadataWithExcluded(this.getClass(), new File("idea/testData/intentions/addPropertyAccessors/getter"), Pattern.compile("^([\\w\\-_]+)\\.(kt|kts)$"), null, true);
             }
 
+            @TestMetadata("caretNotOnName.kt")
+            public void testCaretNotOnName() throws Exception {
+                runTest("idea/testData/intentions/addPropertyAccessors/getter/caretNotOnName.kt");
+            }
+
             @TestMetadata("const.kt")
             public void testConst() throws Exception {
                 runTest("idea/testData/intentions/addPropertyAccessors/getter/const.kt");
@@ -209,6 +219,11 @@ public class HLIntentionTestGenerated extends AbstractHLIntentionTest {
                 KtTestUtil.assertAllTestsPresentByMetadataWithExcluded(this.getClass(), new File("idea/testData/intentions/addPropertyAccessors/setter"), Pattern.compile("^([\\w\\-_]+)\\.(kt|kts)$"), null, true);
             }
 
+            @TestMetadata("caretNotOnName.kt")
+            public void testCaretNotOnName() throws Exception {
+                runTest("idea/testData/intentions/addPropertyAccessors/setter/caretNotOnName.kt");
+            }
+
             @TestMetadata("delegate.kt")
             public void testDelegate() throws Exception {
                 runTest("idea/testData/intentions/addPropertyAccessors/setter/delegate.kt");
diff --git a/idea/testData/intentions/addPropertyAccessors/both/caretNotOnName.kt b/idea/testData/intentions/addPropertyAccessors/both/caretNotOnName.kt
new file mode 100644
index 00000000000..125e3e13bee
--- /dev/null
+++ b/idea/testData/intentions/addPropertyAccessors/both/caretNotOnName.kt
@@ -0,0 +1,4 @@
+// IS_APPLICABLE: false
+class Test {
+    var x = <caret>1
+}
\ No newline at end of file
diff --git a/idea/testData/intentions/addPropertyAccessors/getter/caretNotOnName.kt b/idea/testData/intentions/addPropertyAccessors/getter/caretNotOnName.kt
new file mode 100644
index 00000000000..f92e5bf264b
--- /dev/null
+++ b/idea/testData/intentions/addPropertyAccessors/getter/caretNotOnName.kt
@@ -0,0 +1,4 @@
+// IS_APPLICABLE: false
+class Test {
+    val x = <caret>1
+}
\ No newline at end of file
diff --git a/idea/testData/intentions/addPropertyAccessors/setter/caretNotOnName.kt b/idea/testData/intentions/addPropertyAccessors/setter/caretNotOnName.kt
new file mode 100644
index 00000000000..125e3e13bee
--- /dev/null
+++ b/idea/testData/intentions/addPropertyAccessors/setter/caretNotOnName.kt
@@ -0,0 +1,4 @@
+// IS_APPLICABLE: false
+class Test {
+    var x = <caret>1
+}
\ No newline at end of file
diff --git a/idea/tests/org/jetbrains/kotlin/idea/intentions/IntentionTestGenerated.java b/idea/tests/org/jetbrains/kotlin/idea/intentions/IntentionTestGenerated.java
index ebb92e60720..a592e0d94ac 100644
--- a/idea/tests/org/jetbrains/kotlin/idea/intentions/IntentionTestGenerated.java
+++ b/idea/tests/org/jetbrains/kotlin/idea/intentions/IntentionTestGenerated.java
@@ -1621,6 +1621,11 @@ public class IntentionTestGenerated extends AbstractIntentionTest {
                 KtTestUtil.assertAllTestsPresentByMetadataWithExcluded(this.getClass(), new File("idea/testData/intentions/addPropertyAccessors/both"), Pattern.compile("^([\\w\\-_]+)\\.(kt|kts)$"), null, true);
             }
 
+            @TestMetadata("caretNotOnName.kt")
+            public void testCaretNotOnName() throws Exception {
+                runTest("idea/testData/intentions/addPropertyAccessors/both/caretNotOnName.kt");
+            }
+
             @TestMetadata("delegate.kt")
             public void testDelegate() throws Exception {
                 runTest("idea/testData/intentions/addPropertyAccessors/both/delegate.kt");
@@ -1699,6 +1704,11 @@ public class IntentionTestGenerated extends AbstractIntentionTest {
                 KtTestUtil.assertAllTestsPresentByMetadataWithExcluded(this.getClass(), new File("idea/testData/intentions/addPropertyAccessors/getter"), Pattern.compile("^([\\w\\-_]+)\\.(kt|kts)$"), null, true);
             }
 
+            @TestMetadata("caretNotOnName.kt")
+            public void testCaretNotOnName() throws Exception {
+                runTest("idea/testData/intentions/addPropertyAccessors/getter/caretNotOnName.kt");
+            }
+
             @TestMetadata("const.kt")
             public void testConst() throws Exception {
                 runTest("idea/testData/intentions/addPropertyAccessors/getter/const.kt");
@@ -1782,6 +1792,11 @@ public class IntentionTestGenerated extends AbstractIntentionTest {
                 KtTestUtil.assertAllTestsPresentByMetadataWithExcluded(this.getClass(), new File("idea/testData/intentions/addPropertyAccessors/setter"), Pattern.compile("^([\\w\\-_]+)\\.(kt|kts)$"), null, true);
             }
 
+            @TestMetadata("caretNotOnName.kt")
+            public void testCaretNotOnName() throws Exception {
+                runTest("idea/testData/intentions/addPropertyAccessors/setter/caretNotOnName.kt");
+            }
+
             @TestMetadata("delegate.kt")
             public void testDelegate() throws Exception {
                 runTest("idea/testData/intentions/addPropertyAccessors/setter/delegate.kt");