diff --git a/Tests/test_file_dcx.py b/Tests/test_file_dcx.py
index 5e73fd10f..28ebb91dc 100644
--- a/Tests/test_file_dcx.py
+++ b/Tests/test_file_dcx.py
@@ -42,15 +42,14 @@ class TestFileDcx(PillowTestCase):
 
     def test_eoferror(self):
         im = Image.open(TEST_FILE)
-
         n_frames = im.n_frames
-        while True:
-            n_frames -= 1
-            try:
-                im.seek(n_frames)
-                break
-            except EOFError:
-                self.assertLess(im.tell(), n_frames)
+
+        # Test seeking past the last frame
+        self.assertRaises(EOFError, im.seek, n_frames)
+        self.assertLess(im.tell(), n_frames)
+
+        # Test that seeking to the last frame does not raise an error
+        im.seek(n_frames-1)
 
     def test_seek_too_far(self):
         # Arrange
diff --git a/Tests/test_file_fli.py b/Tests/test_file_fli.py
index 09dd8d8a7..142af3cec 100644
--- a/Tests/test_file_fli.py
+++ b/Tests/test_file_fli.py
@@ -54,24 +54,14 @@ class TestFileFli(PillowTestCase):
 
     def test_eoferror(self):
         im = Image.open(animated_test_file)
-
         n_frames = im.n_frames
-        while True:
-            n_frames -= 1
-            try:
-                im.seek(n_frames)
-                break
-            except EOFError:
-                self.assertLess(im.tell(), n_frames)
 
-    def test_seek_outside(self):
-        # Test negative seek
-        im = Image.open(static_test_file)
-        im.seek(-1)
-        self.assertEqual(im.tell(), 0)
+        # Test seeking past the last frame
+        self.assertRaises(EOFError, im.seek, n_frames)
+        self.assertLess(im.tell(), n_frames)
 
-        # Test seek past end of file
-        self.assertRaises(EOFError, im.seek, 2)
+        # Test that seeking to the last frame does not raise an error
+        im.seek(n_frames-1)
 
     def test_seek_tell(self):
         im = Image.open(animated_test_file)
@@ -91,6 +81,10 @@ class TestFileFli(PillowTestCase):
         layer_number = im.tell()
         self.assertEqual(layer_number, 2)
 
+        im.seek(1)
+        layer_number = im.tell()
+        self.assertEqual(layer_number, 1)
+
 
 if __name__ == '__main__':
     unittest.main()
diff --git a/Tests/test_file_gif.py b/Tests/test_file_gif.py
index f5d244edf..0b52d7b44 100644
--- a/Tests/test_file_gif.py
+++ b/Tests/test_file_gif.py
@@ -223,15 +223,14 @@ class TestFileGif(PillowTestCase):
 
     def test_eoferror(self):
         im = Image.open(TEST_GIF)
-
         n_frames = im.n_frames
-        while True:
-            n_frames -= 1
-            try:
-                im.seek(n_frames)
-                break
-            except EOFError:
-                self.assertLess(im.tell(), n_frames)
+
+        # Test seeking past the last frame
+        self.assertRaises(EOFError, im.seek, n_frames)
+        self.assertLess(im.tell(), n_frames)
+
+        # Test that seeking to the last frame does not raise an error
+        im.seek(n_frames-1)
 
     def test_dispose_none(self):
         img = Image.open("Tests/images/dispose_none.gif")
diff --git a/Tests/test_file_im.py b/Tests/test_file_im.py
index e42197034..c99924767 100644
--- a/Tests/test_file_im.py
+++ b/Tests/test_file_im.py
@@ -32,15 +32,14 @@ class TestFileIm(PillowTestCase):
 
     def test_eoferror(self):
         im = Image.open(TEST_IM)
-
         n_frames = im.n_frames
-        while True:
-            n_frames -= 1
-            try:
-                im.seek(n_frames)
-                break
-            except EOFError:
-                self.assertLess(im.tell(), n_frames)
+
+        # Test seeking past the last frame
+        self.assertRaises(EOFError, im.seek, n_frames)
+        self.assertLess(im.tell(), n_frames)
+
+        # Test that seeking to the last frame does not raise an error
+        im.seek(n_frames-1)
 
     def test_roundtrip(self):
         for mode in ["RGB", "P"]:
diff --git a/Tests/test_file_mpo.py b/Tests/test_file_mpo.py
index b4d0c696e..70bb9b105 100644
--- a/Tests/test_file_mpo.py
+++ b/Tests/test_file_mpo.py
@@ -102,15 +102,14 @@ class TestFileMpo(PillowTestCase):
 
     def test_eoferror(self):
         im = Image.open("Tests/images/sugarshack.mpo")
-
         n_frames = im.n_frames
-        while True:
-            n_frames -= 1
-            try:
-                im.seek(n_frames)
-                break
-            except EOFError:
-                self.assertLess(im.tell(), n_frames)
+
+        # Test seeking past the last frame
+        self.assertRaises(EOFError, im.seek, n_frames)
+        self.assertLess(im.tell(), n_frames)
+
+        # Test that seeking to the last frame does not raise an error
+        im.seek(n_frames-1)
 
     def test_image_grab(self):
         for test_file in test_files:
diff --git a/Tests/test_file_tiff.py b/Tests/test_file_tiff.py
index f8402b47c..3ad8b2bd1 100644
--- a/Tests/test_file_tiff.py
+++ b/Tests/test_file_tiff.py
@@ -250,15 +250,14 @@ class TestFileTiff(PillowTestCase):
 
     def test_eoferror(self):
         im = Image.open('Tests/images/multipage-lastframe.tif')
-
         n_frames = im.n_frames
-        while True:
-            n_frames -= 1
-            try:
-                im.seek(n_frames)
-                break
-            except EOFError:
-                self.assertLess(im.tell(), n_frames)
+
+        # Test seeking past the last frame
+        self.assertRaises(EOFError, im.seek, n_frames)
+        self.assertLess(im.tell(), n_frames)
+
+        # Test that seeking to the last frame does not raise an error
+        im.seek(n_frames-1)
 
     def test_multipage(self):
         # issue #862