diff --git a/lib/super_diff/rspec.rb b/lib/super_diff/rspec.rb
index 14e6f52f..8a2c9dd6 100644
--- a/lib/super_diff/rspec.rb
+++ b/lib/super_diff/rspec.rb
@@ -113,7 +113,7 @@ def self.rspec_version
         ObjectInspection::InspectionTreeBuilders::ObjectHavingAttributes,
         # ObjectInspection::InspectionTreeBuilders::Primitive,
         ObjectInspection::InspectionTreeBuilders::ValueWithin,
-        ObjectInspection::InspectionTreeBuilders::RSpecMatcher
+        ObjectInspection::InspectionTreeBuilders::GenericDescribableMatcher
       )
     end
   end
diff --git a/lib/super_diff/rspec/object_inspection/inspection_tree_builders.rb b/lib/super_diff/rspec/object_inspection/inspection_tree_builders.rb
index d0012258..d14650cf 100644
--- a/lib/super_diff/rspec/object_inspection/inspection_tree_builders.rb
+++ b/lib/super_diff/rspec/object_inspection/inspection_tree_builders.rb
@@ -14,6 +14,10 @@ module InspectionTreeBuilders
           :Double,
           "super_diff/rspec/object_inspection/inspection_tree_builders/double"
         )
+        autoload(
+          :GenericDescribableMatcher,
+          "super_diff/rspec/object_inspection/inspection_tree_builders/generic_describable_matcher"
+        )
         autoload(
           :HashIncluding,
           "super_diff/rspec/object_inspection/inspection_tree_builders/hash_including"
@@ -34,10 +38,6 @@ module InspectionTreeBuilders
           :Primitive,
           "super_diff/rspec/object_inspection/inspection_tree_builders/primitive"
         )
-        autoload(
-          :RSpecMatcher,
-          "super_diff/rspec/object_inspection/inspection_tree_builders/rspec_matcher"
-        )
         autoload(
           :ValueWithin,
           "super_diff/rspec/object_inspection/inspection_tree_builders/value_within"
diff --git a/lib/super_diff/rspec/object_inspection/inspection_tree_builders/rspec_matcher.rb b/lib/super_diff/rspec/object_inspection/inspection_tree_builders/generic_describable_matcher.rb
similarity index 62%
rename from lib/super_diff/rspec/object_inspection/inspection_tree_builders/rspec_matcher.rb
rename to lib/super_diff/rspec/object_inspection/inspection_tree_builders/generic_describable_matcher.rb
index afbdbe22..1a983ca9 100644
--- a/lib/super_diff/rspec/object_inspection/inspection_tree_builders/rspec_matcher.rb
+++ b/lib/super_diff/rspec/object_inspection/inspection_tree_builders/generic_describable_matcher.rb
@@ -2,10 +2,9 @@ module SuperDiff
   module RSpec
     module ObjectInspection
       module InspectionTreeBuilders
-        class RSpecMatcher < SuperDiff::ObjectInspection::InspectionTreeBuilders::Base
+        class GenericDescribableMatcher < SuperDiff::ObjectInspection::InspectionTreeBuilders::Base
           def self.applies_to?(value)
-            value.is_a?(::RSpec::Matchers::BuiltIn::BaseMatcher) ||
-              value.is_a?(::RSpec::Matchers::DSL::Matcher)
+            ::RSpec::Matchers.is_a_describable_matcher?(value)
           end
 
           def call
diff --git a/spec/integration/rspec/generic_describable_matchers_spec.rb b/spec/integration/rspec/generic_describable_matchers_spec.rb
new file mode 100644
index 00000000..f50b5e11
--- /dev/null
+++ b/spec/integration/rspec/generic_describable_matchers_spec.rb
@@ -0,0 +1,177 @@
+require "spec_helper"
+
+RSpec.describe "Integration with describable matchers not handled specially",
+               type: :integration do
+  context "when the expected value contains a built-in matcher (not an aliased matcher)" do
+    it "produces the correct failure message when used in the positive" do
+      as_both_colored_and_uncolored do |color_enabled|
+        snippet = <<~TEST.strip
+            actual = {
+              number: "not a number"
+            }
+            expected = hash_including(
+              number: be_a(Numeric)
+            )
+            expect(actual).to match(expected)
+        TEST
+        program = make_plain_test_program(snippet, color_enabled: color_enabled)
+
+        expected_output =
+          build_expected_output(
+            color_enabled: color_enabled,
+            snippet: "expect(actual).to match(expected)",
+            expectation:
+              proc do
+                line do
+                  plain "Expected "
+                  actual %|{ number: "not a number" }|
+                  plain " to match "
+                  expected "#<a hash including (number: #<be a kind of Numeric>)>"
+                  plain "."
+                end
+              end,
+            diff:
+              proc do
+                plain_line "  {"
+                expected_line "-   number: #<be a kind of Numeric>"
+                actual_line %|+   number: "not a number"|
+                plain_line "  }"
+              end
+          )
+
+        expect(program).to produce_output_when_run(expected_output).in_color(
+          color_enabled
+        )
+      end
+    end
+
+    it "produces the correct failure message when used in the negative" do
+      as_both_colored_and_uncolored do |color_enabled|
+        snippet = <<~TEST.strip
+          actual = {
+            number: 4
+          }
+          expected = hash_including(
+            number: be_a(Numeric)
+          )
+          expect(actual).not_to match(expected)
+        TEST
+        program = make_plain_test_program(snippet, color_enabled: color_enabled)
+
+        expected_output =
+          build_expected_output(
+            color_enabled: color_enabled,
+            snippet: "expect(actual).not_to match(expected)",
+            expectation:
+              proc do
+                line do
+                  plain "Expected "
+                  actual "{ number: 4 }"
+                  plain " not to match "
+                  expected "#<a hash including (number: #<be a kind of Numeric>)>"
+                  plain "."
+                end
+              end
+          )
+
+        expect(program).to produce_output_when_run(expected_output).in_color(
+          color_enabled
+        )
+      end
+    end
+  end
+
+  context "when the expected value contains a custom matcher defined via RSpec::Matchers::DSL" do
+    it "produces the correct failure message" do
+      as_both_colored_and_uncolored do |color_enabled|
+        snippet = <<~TEST.strip
+          actual = {
+            number: "something else"
+          }
+          expected = hash_including(
+            number: failing_custom_matcher_from_dsl(42)
+          )
+          expect(actual).to match(expected)
+        TEST
+        program = make_plain_test_program(snippet, color_enabled: color_enabled)
+
+        expected_output =
+          build_expected_output(
+            color_enabled: color_enabled,
+            snippet: "expect(actual).to match(expected)",
+            newline_before_expectation: true,
+            expectation:
+              proc do
+                line do
+                  plain "Expected "
+                  actual %|{ number: "something else" }|
+                end
+
+                line do
+                  plain "to match "
+                  expected "#<a hash including (number: #<custom matcher defined via the DSL with value 42>)>"
+                end
+              end,
+            diff:
+              proc do
+                plain_line "  {"
+                expected_line "-   number: #<custom matcher defined via the DSL with value 42>"
+                actual_line %|+   number: "something else"|
+                plain_line "  }"
+              end
+          )
+
+        expect(program).to produce_output_when_run(expected_output).in_color(
+          color_enabled
+        )
+      end
+    end
+  end
+
+  context "when the expected value contains a custom matcher defined from scratch" do
+    it "produces the correct failure message" do
+      as_both_colored_and_uncolored do |color_enabled|
+        snippet = <<~TEST.strip
+          actual = {
+            number: "something else"
+          }
+          expected = hash_including(
+            number: failing_custom_matcher_from_scratch(42)
+          )
+          expect(actual).to match(expected)
+        TEST
+        program = make_plain_test_program(snippet, color_enabled: color_enabled)
+
+        expected_output =
+          build_expected_output(
+            color_enabled: color_enabled,
+            snippet: "expect(actual).to match(expected)",
+            newline_before_expectation: true,
+            expectation:
+              proc do
+                line do
+                  plain "Expected "
+                  actual %|{ number: "something else" }|
+                end
+
+                line do
+                  plain "to match "
+                  expected "#<a hash including (number: #<custom matcher defined from scratch with value 42>)>"
+                end
+              end,
+            diff:
+              proc do
+                plain_line "  {"
+                expected_line "-   number: #<custom matcher defined from scratch with value 42>"
+                actual_line %|+   number: "something else"|
+                plain_line "  }"
+              end
+          )
+
+        expect(program).to produce_output_when_run(expected_output).in_color(
+          color_enabled
+        )
+      end
+    end
+  end
+end
diff --git a/spec/integration/rspec/unhandled_matcher_spec.rb b/spec/integration/rspec/unhandled_matcher_spec.rb
deleted file mode 100644
index 999305ec..00000000
--- a/spec/integration/rspec/unhandled_matcher_spec.rb
+++ /dev/null
@@ -1,86 +0,0 @@
-require "spec_helper"
-
-RSpec.describe "Integration with built-in RSpec matchers", type: :integration do
-  context "when the expected value contains a built-in matcher" do
-    context "that fails" do
-      it "produces the correct failure message when used in the negative" do
-        as_both_colored_and_uncolored do |color_enabled|
-          snippet = <<~TEST.strip
-            actual = {
-              number: 4
-            }
-            expected = hash_including(
-              number: be_a(Numeric)
-            )
-            expect(actual).not_to match(expected)
-          TEST
-          program =
-            make_plain_test_program(snippet, color_enabled: color_enabled)
-
-          expected_output =
-            build_expected_output(
-              color_enabled: color_enabled,
-              snippet: "expect(actual).not_to match(expected)",
-              expectation:
-                proc do
-                  line do
-                    plain "Expected "
-                    actual "{ number: 4 }"
-                    plain " not to match "
-                    expected "#<a hash including (number: #<be a kind of Numeric>)>"
-                    plain "."
-                  end
-                end
-            )
-
-          expect(program).to produce_output_when_run(expected_output).in_color(
-            color_enabled
-          )
-        end
-      end
-
-      it "produces the correct failure message when used in the positive" do
-        as_both_colored_and_uncolored do |color_enabled|
-          snippet = <<~TEST.strip
-            actual = {
-              number: "not a number"
-            }
-            expected = hash_including(
-              number: be_a(Numeric)
-            )
-            expect(actual).to match(expected)
-          TEST
-          program =
-            make_plain_test_program(snippet, color_enabled: color_enabled)
-
-          expected_output =
-            build_expected_output(
-              color_enabled: color_enabled,
-              snippet: "expect(actual).to match(expected)",
-              expectation:
-                proc do
-                  line do
-                    plain "Expected "
-                    actual %|{ number: "not a number" }|
-                    plain " to match "
-                    expected "#<a hash including (number: #<be a kind of Numeric>)>"
-                    plain "."
-                  end
-                end,
-              diff:
-                proc do
-                  plain_line "  {"
-                  expected_line "-   number: #<be a kind of Numeric>"
-                  actual_line %|+   number: "not a number"|
-                  plain_line "  }"
-                end
-            )
-
-          expect(program).to produce_output_when_run(expected_output).in_color(
-            color_enabled
-          )
-        end
-      end
-    end
-  end
-end
diff --git a/spec/support/integration/matchers.rb b/spec/support/integration/matchers.rb
index 8c2c8da0..870273bb 100644
--- a/spec/support/integration/matchers.rb
+++ b/spec/support/integration/matchers.rb
@@ -32,6 +32,40 @@ def pass_with_singleline_failure_message
       PassWithSinglelineFailureMessageMatcher.new
     end
 
+    RSpec::Matchers.define :failing_custom_matcher_from_dsl do |value|
+      match { false }
+
+      description do
+        "custom matcher defined via the DSL with value #{value.inspect}"
+      end
+    end
+
+    def failing_custom_matcher_from_scratch(value)
+      FailingCustomMatcherFromScratch.new(value)
+    end
+
+    class FailingCustomMatcherFromScratch
+      def initialize(value)
+        @value = value
+      end
+
+      def matches?(_)
+        false
+      end
+
+      def description
+        "custom matcher defined from scratch with value #{value.inspect}"
+      end
+
+      def failure_message
+        "Expected custom matcher not to fail, but did"
+      end
+
+      private
+
+      attr_reader :value
+    end
+
     class FailWithIndentedMultilineFailureMessageMatcher
       def matches?(_)
         false