diff --git a/CHANGELOG.md b/CHANGELOG.md
index a4d05ff11bf..ef20d04856e 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -20,6 +20,7 @@
 * [#6778](https://github.com/rubocop-hq/rubocop/issues/6778): Fix a false positive in `Style/HashSyntax` cop when a hash key is an interpolated string and EnforcedStyle is ruby19_no_mixed_keys. ([@tatsuyafw][])
 * [#6902](https://github.com/rubocop-hq/rubocop/issues/6902): Fix a bug where `Naming/RescuedExceptionsVariableName` would handle an only first rescue for multiple rescue groups. ([@tatsuyafw][])
 * [#6860](https://github.com/rubocop-hq/rubocop/issues/6860): Prevent auto-correct conflict of `Style/InverseMethods` and `Style/Not`. ([@hoshinotsuyoshi][])
+* [#6935](https://github.com/rubocop-hq/rubocop/issues/6935): `Layout/AccessModifierIndentation` should ignore access modifiers that apply to specific methods. ([@deivid-rodriguez][])
 
 ### Changes
 
diff --git a/lib/rubocop/cop/layout/access_modifier_indentation.rb b/lib/rubocop/cop/layout/access_modifier_indentation.rb
index 61807bd6a92..07375f910d9 100644
--- a/lib/rubocop/cop/layout/access_modifier_indentation.rb
+++ b/lib/rubocop/cop/layout/access_modifier_indentation.rb
@@ -3,8 +3,9 @@
 module RuboCop
   module Cop
     module Layout
-      # Modifiers should be indented as deep as method definitions, or as deep
-      # as the class/module keyword, depending on configuration.
+      # Bare access modifiers (those not applying to specific methods) should be
+      # indented as deep as method definitions, or as deep as the class/module
+      # keyword, depending on configuration.
       #
       # @example EnforcedStyle: indent (default)
       #   # bad
@@ -67,7 +68,8 @@ def check_body(body, node)
           return if body.nil? # Empty class etc.
           return unless body.begin_type?
 
-          modifiers = body.each_child_node(:send).select(&:access_modifier?)
+          modifiers = body.each_child_node(:send)
+                          .select(&:bare_access_modifier?)
           end_range = node.loc.end
 
           modifiers.each { |modifier| check_modifier(modifier, end_range) }
diff --git a/manual/cops_layout.md b/manual/cops_layout.md
index 1cdfef01235..a0e6c975700 100644
--- a/manual/cops_layout.md
+++ b/manual/cops_layout.md
@@ -6,8 +6,9 @@ Enabled by default | Safe | Supports autocorrection | VersionAdded | VersionChan
 --- | --- | --- | --- | ---
 Enabled | Yes | Yes  | 0.49 | -
 
-Modifiers should be indented as deep as method definitions, or as deep
-as the class/module keyword, depending on configuration.
+Bare access modifiers (those not applying to specific methods) should be
+indented as deep as method definitions, or as deep as the class/module
+keyword, depending on configuration.
 
 ### Examples
 
diff --git a/spec/rubocop/cop/layout/access_modifier_indentation_spec.rb b/spec/rubocop/cop/layout/access_modifier_indentation_spec.rb
index 3445bd292d1..1a9d06210aa 100644
--- a/spec/rubocop/cop/layout/access_modifier_indentation_spec.rb
+++ b/spec/rubocop/cop/layout/access_modifier_indentation_spec.rb
@@ -306,6 +306,25 @@ def test; end
       RUBY
     end
 
+    it 'accepts private with argument indented to method depth in a class' do
+      expect_no_offenses(<<-RUBY.strip_indent)
+        class Test
+
+          def test; end
+          private :test
+        end
+      RUBY
+    end
+
+    it 'accepts private def indented to method depth in a class' do
+      expect_no_offenses(<<-RUBY.strip_indent)
+        class Test
+
+          private def test; end
+        end
+      RUBY
+    end
+
     it 'registers offense for private indented to method depth in a module' do
       expect_offense(<<-RUBY.strip_indent)
         module Test
@@ -318,6 +337,25 @@ def test; end
       RUBY
     end
 
+    it 'accepts private with argument indented to method depth in a module' do
+      expect_no_offenses(<<-RUBY.strip_indent)
+        module Test
+
+          def test; end
+          private :test
+        end
+      RUBY
+    end
+
+    it 'accepts private def indented to method depth in a module' do
+      expect_no_offenses(<<-RUBY.strip_indent)
+        module Test
+
+          private def test; end
+        end
+      RUBY
+    end
+
     it 'registers offense for module fn indented to method depth in a module' do
       expect_offense(<<-RUBY.strip_indent)
         module Test
@@ -330,7 +368,27 @@ def test; end
       RUBY
     end
 
-    it 'registers offense for private indented to method depth in singleton' \
+    it 'accepts module fn with argument indented to ' \
+       'method depth in a module' do
+      expect_no_offenses(<<-RUBY.strip_indent)
+        module Test
+
+          def test; end
+          module_function :test
+        end
+      RUBY
+    end
+
+    it 'accepts module fn def indented to method depth in a module' do
+      expect_no_offenses(<<-RUBY.strip_indent)
+        module Test
+
+          module_function def test; end
+        end
+      RUBY
+    end
+
+    it 'registers offense for private indented to method depth in singleton ' \
        'class' do
       expect_offense(<<-RUBY.strip_indent)
         class << self
@@ -343,6 +401,26 @@ def test; end
       RUBY
     end
 
+    it 'accepts private with argument indented to ' \
+       'method depth in singleton class' do
+      expect_no_offenses(<<-RUBY.strip_indent)
+        class << self
+
+          def test; end
+          private :test
+        end
+      RUBY
+    end
+
+    it 'accepts private def indented to method depth in singleton class' do
+      expect_no_offenses(<<-RUBY.strip_indent)
+        class << self
+
+          private def test; end
+        end
+      RUBY
+    end
+
     it 'registers offense for private indented to method depth in class ' \
        'defined with Class.new' do
       expect_offense(<<-RUBY.strip_indent)
@@ -356,6 +434,27 @@ def test; end
       RUBY
     end
 
+    it 'accepts private with argument indented to method depth in class ' \
+       'defined with Class.new' do
+      expect_no_offenses(<<-RUBY.strip_indent)
+        Test = Class.new do
+
+          def test; end
+          private :test
+        end
+      RUBY
+    end
+
+    it 'accepts private def indented to method depth in class defined with ' \
+       'Class.new' do
+      expect_no_offenses(<<-RUBY.strip_indent)
+        Test = Class.new do
+
+          private def test; end
+        end
+      RUBY
+    end
+
     it 'registers offense for private indented to method depth in module ' \
        'defined with Module.new' do
       expect_offense(<<-RUBY.strip_indent)
@@ -369,6 +468,27 @@ def test; end
       RUBY
     end
 
+    it 'accepts private with argument indented to method depth in module ' \
+       'defined with Module.new' do
+      expect_no_offenses(<<-RUBY.strip_indent)
+        Test = Module.new do
+
+          def test; end
+          private :test
+        end
+      RUBY
+    end
+
+    it 'accepts private def indented to method depth in module defined with ' \
+       'Module.new' do
+      expect_no_offenses(<<-RUBY.strip_indent)
+        Test = Module.new do
+
+          private def test; end
+        end
+      RUBY
+    end
+
     it 'accepts private indented to the containing class indent level' do
       expect_no_offenses(<<-RUBY.strip_indent)
         class Test