diff --git a/PIL/Jpeg2KImagePlugin.py b/PIL/Jpeg2KImagePlugin.py
index cd72107a8..f57f4a784 100644
--- a/PIL/Jpeg2KImagePlugin.py
+++ b/PIL/Jpeg2KImagePlugin.py
@@ -169,14 +169,14 @@ class Jpeg2KImageFile(ImageFile.ImageFile):
         if self.reduce:
             power = 1 << self.reduce
             adjust = power >> 1
-            self.size = ((self.size[0] + adjust) / power,
-                         (self.size[1] + adjust) / power)
+            self.size = (int((self.size[0] + adjust) / power),
+                         int((self.size[1] + adjust) / power))
 
         if self.tile:
             # Update the reduce and layers settings
             t = self.tile[0]
             t3 = (t[3][0], self.reduce, self.layers, t[3][3])
-            self.tile = [(t[0], t[1], t[2], t3)]
+            self.tile = [(t[0], (0, 0) + self.size, t[2], t3)]
         
         ImageFile.ImageFile.load(self)
         
diff --git a/Tests/run.py b/Tests/run.py
index 02b633c90..01a3f3603 100644
--- a/Tests/run.py
+++ b/Tests/run.py
@@ -2,7 +2,7 @@ from __future__ import print_function
 
 # minimal test runner
 
-import glob, os, os.path, sys, tempfile
+import glob, os, os.path, sys, tempfile, re
 
 try:
     root = os.path.dirname(__file__)
@@ -38,6 +38,8 @@ skipped = []
 python_options = " ".join(python_options)
 tester_options = " ".join(tester_options)
 
+ignore_re = re.compile('^ignore: (.*)$', re.MULTILINE)
+
 for file in files:
     test, ext = os.path.splitext(os.path.basename(file))
     if include and test not in include:
@@ -48,7 +50,30 @@ for file in files:
     out = os.popen("%s %s -u %s %s 2>&1" % (
             sys.executable, python_options, file, tester_options
             ))
-    result = out.read().strip()
+    result = out.read()
+
+    # Extract any ignore patterns
+    ignore_pats = ignore_re.findall(result)
+    result = ignore_re.sub('', result)
+
+    try:
+        def fix_re(p):
+            if not p.startswith('^'):
+                p = '^' + p
+            if not p.endswith('$'):
+                p = p + '$'
+            return p
+        
+        ignore_res = [re.compile(fix_re(p), re.MULTILINE) for p in ignore_pats]
+    except:
+        print('(bad ignore patterns %r)' % ignore_pats)
+        ignore_res = []
+
+    for r in ignore_res:
+        result = r.sub('', result)
+
+    result = result.strip()
+    
     if result == "ok":
         result = None
     elif result == "skip":
diff --git a/Tests/test_file_jpeg2k.py b/Tests/test_file_jpeg2k.py
index 1230f7977..b11e5e6ab 100644
--- a/Tests/test_file_jpeg2k.py
+++ b/Tests/test_file_jpeg2k.py
@@ -8,6 +8,10 @@ codecs = dir(Image.core)
 if "jpeg2k_encoder" not in codecs or "jpeg2k_decoder" not in codecs:
     skip('JPEG 2000 support not available')
 
+# OpenJPEG 2.0.0 outputs this debugging message sometimes; we should
+# ignore it---it doesn't represent a test failure.
+ignore('Not enough memory to handle tile data')
+
 test_card = Image.open('Tests/images/test-card.png')
 test_card.load()
 
diff --git a/Tests/tester.py b/Tests/tester.py
index 2c6fa071c..d4309e3e6 100644
--- a/Tests/tester.py
+++ b/Tests/tester.py
@@ -260,6 +260,11 @@ def skip(msg=None):
     print("skip")
     os._exit(0) # don't run exit handlers
 
+def ignore(pattern):
+    """Tells the driver to ignore messages matching the pattern, for the
+    duration of the current test."""
+    print('ignore: %s' % pattern)
+
 def _setup():
     global _logfile
     def report():
diff --git a/libImaging/Incremental.c b/libImaging/Incremental.c
index 9574d51a8..9e7fb38ec 100644
--- a/libImaging/Incremental.c
+++ b/libImaging/Incremental.c
@@ -130,6 +130,9 @@ codec_thread(void *ptr)
 static void
 flush_stream(ImagingIncrementalCodec codec)
 {
+  UINT8 *buffer;
+  size_t bytes;
+
   /* This is to flush data from the write buffer for a seekable write
      codec. */
   if (codec->read_or_write != INCREMENTAL_CODEC_WRITE
@@ -140,8 +143,8 @@ flush_stream(ImagingIncrementalCodec codec)
 
   DEBUG("flushing data\n");
 
-  UINT8 *buffer = codec->stream.buffer;
-  size_t bytes = codec->stream.ptr - codec->stream.buffer;
+  buffer = codec->stream.buffer;
+  bytes = codec->stream.ptr - codec->stream.buffer;
 
   codec->state->errcode = 0;
   codec->seekable = INCREMENTAL_CODEC_NOT_SEEKABLE;
@@ -645,6 +648,8 @@ off_t
 ImagingIncrementalCodecSeek(ImagingIncrementalCodec codec,
                             off_t bytes)
 {
+  off_t buffered;
+
   DEBUG("seeking (going to %llu bytes)\n", (unsigned long long)bytes);
 
   if (codec->stream.fd >= 0)
@@ -660,7 +665,7 @@ ImagingIncrementalCodecSeek(ImagingIncrementalCodec codec,
     return -1;
   }
     
-  off_t buffered = codec->stream.top - codec->stream.buffer;
+  buffered = codec->stream.top - codec->stream.buffer;
 
   if (bytes <= buffered) {
     DEBUG("seek within buffer\n");
diff --git a/libImaging/Jpeg2KDecode.c b/libImaging/Jpeg2KDecode.c
index dd20dc738..6b6176c78 100644
--- a/libImaging/Jpeg2KDecode.c
+++ b/libImaging/Jpeg2KDecode.c
@@ -230,7 +230,7 @@ j2ku_graya_la(opj_image_t *in, const JPEG2KTILEINFO *tileinfo,
         const UINT8 *adata = &atiledata[acsiz * y * w];
         UINT8 *row = (UINT8 *)im->image[y0 + y] + x0 * 4;
         for (x = 0; x < w; ++x) {
-            UINT32 word = 0, aword = 0;
+            UINT32 word = 0, aword = 0, byte;
 
             switch (csiz) {
             case 1: word = *data++; break;
@@ -244,7 +244,7 @@ j2ku_graya_la(opj_image_t *in, const JPEG2KTILEINFO *tileinfo,
             case 4: aword = *(const UINT32 *)adata; adata += 4; break;
             }
 
-            UINT8 byte = j2ku_shift(offset + word, shift);
+            byte = j2ku_shift(offset + word, shift);
             row[0] = row[1] = row[2] = byte;
             row[3] = j2ku_shift(aoffset + aword, ashift);
             row += 4;
@@ -552,9 +552,7 @@ j2k_decode_entry(Imaging im, ImagingCodecState state,
     }
     
     for (n = 1; n < image->numcomps; ++n) {
-        /* Check that the sample frequency is uniform */
-        if (image->comps[0].dx != image->comps[n].dx
-            || image->comps[0].dy != image->comps[n].dy) {
+        if (image->comps[n].dx != 1 || image->comps[n].dy != 1) {
             state->errcode = IMAGING_CODEC_BROKEN;
             state->state = J2K_STATE_FAILED;
             goto quick_exit;
@@ -612,6 +610,7 @@ j2k_decode_entry(Imaging im, ImagingCodecState state,
     for (;;) {
         JPEG2KTILEINFO tile_info;
         OPJ_BOOL should_continue;
+        unsigned correction = (1 << params.cp_reduce) - 1;
 
         if (!opj_read_tile_header(codec,
                                   stream,
@@ -629,6 +628,13 @@ j2k_decode_entry(Imaging im, ImagingCodecState state,
         if (!should_continue)
             break;
 
+        /* Adjust the tile co-ordinates based on the reduction (OpenJPEG
+           doesn't do this for us) */
+        tile_info.x0 = (tile_info.x0 + correction) >> context->reduce;
+        tile_info.y0 = (tile_info.y0 + correction) >> context->reduce;
+        tile_info.x1 = (tile_info.x1 + correction) >> context->reduce;
+        tile_info.y1 = (tile_info.y1 + correction) >> context->reduce;
+
         if (buffer_size < tile_info.data_size) {
             UINT8 *new = realloc (state->buffer, tile_info.data_size);
             if (!new) {