diff --git a/docs/source/media.rst b/docs/source/media.rst
index 53c9f293..e0a4c3f9 100644
--- a/docs/source/media.rst
+++ b/docs/source/media.rst
@@ -66,7 +66,7 @@ Moving Media
 
 You should taking caution if manually changing a media record's attributes, as your record and file could go out of sync.
 
-You can change the location of a media file on disk. You cannot move a media to a different disk this way.
+You can change the location of a media file on disk.
 
 ::
 
@@ -74,17 +74,19 @@ You can change the location of a media file on disk. You cannot move a media to
 	$media->move('new/directory');
 	$media->move('new/directory', 'new-filename');
 	$media->rename('new-filename');
+    $media->moveToDisk('uploads', 'new/directory', 'new-filename');
 
 Copying Media
 ---------------------
 
-You can duplicate a media file to a different location on disk with the ``copyTo()`` method. Doing so will create a new `Media` record for the new file. If a filename is not provided, the new file will copy the original filename. 
+You can duplicate a media file to a different location on disk with the ``copyTo()`` method. Doing so will create a new `Media` record for the new file. If a filename is not provided, the new file will copy the original filename.
 
 ::
 
     <?php
     $newMedia = $media->copyTo('new/directory');
     $newMedia = $media->copyTo('new/directory', 'new-filename');
+    $newMedia = $media->copyToDisk('uploads', 'new/directory', 'new-filename');
 
 Deleting Media
 ---------------------
diff --git a/src/MediaMover.php b/src/MediaMover.php
index f0a7a4d3..8ac9980b 100644
--- a/src/MediaMover.php
+++ b/src/MediaMover.php
@@ -87,6 +87,7 @@ public function moveToDisk(Media $media, string $disk, string $directory, string
 
         try {
             $targetStorage->put($targetPath, $currentStorage->readStream($media->getDiskPath()));
+            $targetStorage->setVisibility($targetPath, $currentStorage->getVisibility($media->getDiskPath()));
             $currentStorage->delete($media->getDiskPath());
         } catch (FileNotFoundException $e) {
             throw MediaMoveException::fileNotFound($media->disk, $media->getDiskPath(), $e);
@@ -172,6 +173,7 @@ public function copyToDisk(Media $media, string $disk, string $directory, string
 
         try {
             $targetStorage->put($targetPath, $currentStorage->readStream($media->getDiskPath()));
+            $targetStorage->setVisibility($targetPath, $currentStorage->getVisibility($media->getDiskPath()));
         } catch (FileNotFoundException $e) {
             throw MediaMoveException::fileNotFound($media->disk, $media->getDiskPath(), $e);
         }
diff --git a/tests/integration/MediaTest.php b/tests/integration/MediaTest.php
index fcb2b976..15264a05 100644
--- a/tests/integration/MediaTest.php
+++ b/tests/integration/MediaTest.php
@@ -282,7 +282,7 @@ public function test_it_throws_an_exception_if_moving_to_existing_file()
         $media1->move('', 'bar.baz');
     }
 
-    public function test_it_can_be_moved_to_another_disk()
+    public function test_it_can_be_moved_to_another_disk_public()
     {
         $this->useFilesystem('tmp');
         $this->useFilesystem('uploads');
@@ -297,15 +297,72 @@ public function test_it_can_be_moved_to_another_disk()
         ]);
         $original_path = $media->getAbsolutePath();
         $this->seedFileForMedia($media);
+        $media->makePublic();
+
+        $media->moveToDisk('uploads', 'alpha/beta', 'gamma');
+        $this->assertEquals('uploads', $media->disk);
+        $this->assertEquals('alpha/beta/gamma.baz', $media->getDiskPath());
+        $this->assertTrue($media->fileExists());
+        $this->assertFalse(file_exists($original_path));
+        $this->assertTrue($media->isVisible());
+    }
+
+    public function test_it_can_be_moved_to_another_disk_private()
+    {
+        $this->useFilesystem('tmp');
+        $this->useFilesystem('uploads');
+
+        $this->useDatabase();
+
+        $media = $this->makeMedia([
+            'disk' => 'tmp',
+            'directory' => 'foo',
+            'filename' => 'bar',
+            'extension' => 'baz'
+        ]);
+        $original_path = $media->getAbsolutePath();
+        $this->seedFileForMedia($media);
+        $media->makePrivate();
 
         $media->moveToDisk('uploads', 'alpha/beta', 'gamma');
         $this->assertEquals('uploads', $media->disk);
         $this->assertEquals('alpha/beta/gamma.baz', $media->getDiskPath());
         $this->assertTrue($media->fileExists());
         $this->assertFalse(file_exists($original_path));
+        $this->assertFalse($media->isVisible());
+    }
+
+    public function test_it_can_be_copied_to_another_disk_public()
+    {
+        $this->useFilesystem('tmp');
+        $this->useFilesystem('uploads');
+
+        $this->useDatabase();
+
+        $media = $this->makeMedia([
+            'disk' => 'tmp',
+            'directory' => 'foo',
+            'filename' => 'bar',
+            'extension' => 'baz'
+        ]);
+        $original_path = $media->getAbsolutePath();
+        $this->seedFileForMedia($media);
+        $media->makePublic();
+
+        $newMedia = $media->copyToDisk('uploads', 'alpha/beta', 'gamma');
+        $this->assertEquals('uploads', $newMedia->disk);
+        $this->assertEquals('alpha/beta/gamma.baz', $newMedia->getDiskPath());
+        $this->assertTrue($newMedia->fileExists());
+        $this->assertTrue($newMedia->isVisible());
+
+        //original should be unchanged
+        $this->assertEquals('tmp', $media->disk);
+        $this->assertEquals('foo/bar.baz', $media->getDiskPath());
+        $this->assertTrue($media->fileExists());
+        $this->assertTrue($media->isVisible());
     }
 
-    public function test_it_can_be_copied_to_another_disk()
+    public function test_it_can_be_copied_to_another_disk_private()
     {
         $this->useFilesystem('tmp');
         $this->useFilesystem('uploads');
@@ -320,16 +377,19 @@ public function test_it_can_be_copied_to_another_disk()
         ]);
         $original_path = $media->getAbsolutePath();
         $this->seedFileForMedia($media);
+        $media->makePrivate();
 
         $newMedia = $media->copyToDisk('uploads', 'alpha/beta', 'gamma');
         $this->assertEquals('uploads', $newMedia->disk);
         $this->assertEquals('alpha/beta/gamma.baz', $newMedia->getDiskPath());
         $this->assertTrue($newMedia->fileExists());
+        $this->assertFalse($newMedia->isVisible());
 
         //original should be unchanged
         $this->assertEquals('tmp', $media->disk);
         $this->assertEquals('foo/bar.baz', $media->getDiskPath());
         $this->assertTrue($media->fileExists());
+        $this->assertFalse($media->isVisible());
     }
 
     public function test_it_can_access_file_contents()