diff --git a/Tests/test_file_jpeg2k.py b/Tests/test_file_jpeg2k.py
index b9422c76a..52e9f8853 100644
--- a/Tests/test_file_jpeg2k.py
+++ b/Tests/test_file_jpeg2k.py
@@ -411,29 +411,30 @@ def test_crashes(test_file):
 
 @skip_unless_feature_version("jpg_2000", "2.4.0")
 def test_plt_marker():
-    # Search the start of the codesteam for the PLT box (id 0xFF58)
+    # Search the start of the codesteam for PLT
     out = BytesIO()
     test_card.save(out, "JPEG2000", no_jp2=True, plt=True)
     out.seek(0)
     while True:
-        box_bytes = out.read(2)
-        if not box_bytes:
+        marker = out.read(2)
+        if not marker:
             # End of steam encountered and no PLT or SOD
             break
 
-        jp2_boxid = _binary.i16be(box_bytes)
+        jp2_boxid = _binary.i16be(marker)
         if jp2_boxid == 0xFF4F:
-            # No length specifier for main header
+            # SOC has no length
             continue
         elif jp2_boxid == 0xFF58:
-            # This is the PLT box we're looking for
+            # PLT
             return
         elif jp2_boxid == 0xFF93:
-            # SOD box encountered and no PLT, so it wasn't found
+            # SOD without finding PLT first
             break
 
-        jp2_boxlength = _binary.i16be(out.read(2))
-        out.seek(jp2_boxlength - 2, os.SEEK_CUR)
+        hdr = out.read(2)
+        length = _binary.i16be(hdr)
+        out.seek(length - 2, os.SEEK_CUR)
 
-    # The PLT box wasn't found
+    # PLT wasn't found
     raise ValueError
diff --git a/src/PIL/Jpeg2KImagePlugin.py b/src/PIL/Jpeg2KImagePlugin.py
index e7d91c818..9309768ba 100644
--- a/src/PIL/Jpeg2KImagePlugin.py
+++ b/src/PIL/Jpeg2KImagePlugin.py
@@ -17,7 +17,7 @@ import io
 import os
 import struct
 
-from . import Image, ImageFile
+from . import Image, ImageFile, _binary
 
 
 class BoxReader:
@@ -99,7 +99,7 @@ def _parse_codestream(fp):
     count from the SIZ marker segment, returning a PIL (size, mode) tuple."""
 
     hdr = fp.read(2)
-    lsiz = struct.unpack(">H", hdr)[0]
+    lsiz = _binary.i16be(hdr)
     siz = hdr + fp.read(lsiz - 2)
     lsiz, rsiz, xsiz, ysiz, xosiz, yosiz, _, _, _, _, csiz = struct.unpack_from(
         ">HHIIIIIIIIH", siz
@@ -258,7 +258,7 @@ class Jpeg2KImageFile(ImageFile.ImageFile):
 
     def _parse_comment(self):
         hdr = self.fp.read(2)
-        length = struct.unpack(">H", hdr)[0]
+        length = _binary.i16be(hdr)
         self.fp.seek(length - 2, os.SEEK_CUR)
 
         while True:
@@ -270,7 +270,7 @@ class Jpeg2KImageFile(ImageFile.ImageFile):
                 # Start of tile or end of codestream
                 break
             hdr = self.fp.read(2)
-            length = struct.unpack(">H", hdr)[0]
+            length = _binary.i16be(hdr)
             if typ == 0x64:
                 # Comment
                 self.info["comment"] = self.fp.read(length - 2)[2:]