diff --git a/core/src/main/java/org/testcontainers/utility/DockerImageName.java b/core/src/main/java/org/testcontainers/utility/DockerImageName.java
index e3a35855bf8..7010e4f3704 100644
--- a/core/src/main/java/org/testcontainers/utility/DockerImageName.java
+++ b/core/src/main/java/org/testcontainers/utility/DockerImageName.java
@@ -233,15 +233,13 @@ public DockerImageName asCompatibleSubstituteFor(DockerImageName otherImageName)
      * @return whether this image has declared compatibility.
      */
     public boolean isCompatibleWith(DockerImageName other) {
-        // Make sure we always compare against a version of the image name containing the LIBRARY_PREFIX
-        String finalImageName;
-        if (this.repository.startsWith(LIBRARY_PREFIX)) {
-            finalImageName = this.repository;
-        } else {
-            finalImageName = LIBRARY_PREFIX + this.repository;
+        if (other.equals(this)) {
+            return true;
         }
-        DockerImageName imageWithLibraryPrefix = DockerImageName.parse(finalImageName);
-        if (other.equals(this) || imageWithLibraryPrefix.equals(this)) {
+
+        // 'library/foo' and 'foo' refer to the same official Docker Hub image, so compare both
+        // names normalized to include the LIBRARY_PREFIX.
+        if (withLibraryPrefix(other).equals(withLibraryPrefix(this))) {
             return true;
         }
 
@@ -252,6 +250,13 @@ public boolean isCompatibleWith(DockerImageName other) {
         return this.compatibleSubstituteFor.isCompatibleWith(other);
     }
 
+    private static DockerImageName withLibraryPrefix(DockerImageName image) {
+        if (!image.registry.isEmpty() || image.repository.startsWith(LIBRARY_PREFIX)) {
+            return image;
+        }
+        return image.withRepository(LIBRARY_PREFIX + image.repository);
+    }
+
     /**
      * Behaves as {@link DockerImageName#isCompatibleWith(DockerImageName)} but throws an exception
      * rather than returning false if a mismatch is detected.
diff --git a/core/src/test/java/org/testcontainers/utility/DockerImageNameCompatibilityTest.java b/core/src/test/java/org/testcontainers/utility/DockerImageNameCompatibilityTest.java
index dc7bf9ba1ab..1cac92b38af 100644
--- a/core/src/test/java/org/testcontainers/utility/DockerImageNameCompatibilityTest.java
+++ b/core/src/test/java/org/testcontainers/utility/DockerImageNameCompatibilityTest.java
@@ -97,6 +97,54 @@ void testAssertMethodAcceptsCompatibleLibraryPrefix() {
         subject.assertCompatibleWith(DockerImageName.parse("foo"));
     }
 
+    @Test
+    void testLibraryPrefixedImageIsNotCompatibleWithDifferentImage() {
+        DockerImageName subject = DockerImageName.parse("library/foo:1.2.3");
+
+        assertThat(subject.isCompatibleWith(DockerImageName.parse("bar"))).as("library/foo:1.2.3 != bar").isFalse();
+        assertThat(subject.isCompatibleWith(DockerImageName.parse("repo/bar")))
+            .as("library/foo:1.2.3 != repo/bar")
+            .isFalse();
+        assertThat(subject.isCompatibleWith(DockerImageName.parse("library/bar")))
+            .as("library/foo:1.2.3 != library/bar")
+            .isFalse();
+    }
+
+    @Test
+    void testLibraryPrefixIsInterchangeable() {
+        assertThat(DockerImageName.parse("library/foo").isCompatibleWith(DockerImageName.parse("foo")))
+            .as("library/foo ~= foo")
+            .isTrue();
+        assertThat(DockerImageName.parse("foo").isCompatibleWith(DockerImageName.parse("library/foo")))
+            .as("foo ~= library/foo")
+            .isTrue();
+        assertThat(DockerImageName.parse("library/foo:1.2.3").isCompatibleWith(DockerImageName.parse("foo")))
+            .as("library/foo:1.2.3 ~= foo")
+            .isTrue();
+        assertThat(DockerImageName.parse("foo:1.2.3").isCompatibleWith(DockerImageName.parse("library/foo")))
+            .as("foo:1.2.3 ~= library/foo")
+            .isTrue();
+        assertThat(DockerImageName.parse("library/foo:1.2.3").isCompatibleWith(DockerImageName.parse("foo:1.2.3")))
+            .as("library/foo:1.2.3 ~= foo:1.2.3")
+            .isTrue();
+        assertThat(DockerImageName.parse("library/foo:1.2.3").isCompatibleWith(DockerImageName.parse("foo:4.5.6")))
+            .as("library/foo:1.2.3 != foo:4.5.6")
+            .isFalse();
+        assertThat(DockerImageName.parse("some.registry/foo").isCompatibleWith(DockerImageName.parse("library/foo")))
+            .as("some.registry/foo != library/foo")
+            .isFalse();
+    }
+
+    @Test
+    void testLibraryPrefixedImageWithClaimedCompatibility() {
+        DockerImageName subject = DockerImageName.parse("library/foo:1.2.3").asCompatibleSubstituteFor("bar");
+
+        assertThat(subject.isCompatibleWith(DockerImageName.parse("bar"))).as("library/foo:1.2.3(bar) ~= bar").isTrue();
+        assertThat(subject.isCompatibleWith(DockerImageName.parse("fizz")))
+            .as("library/foo:1.2.3(bar) != fizz")
+            .isFalse();
+    }
+
     @Test
     void testAssertMethodRejectsIncompatible() {
         DockerImageName subject = DockerImageName.parse("foo");