diff --git a/delta_performer.cc b/delta_performer.cc
index 0a2a943..ae1f7e5 100644
--- a/delta_performer.cc
+++ b/delta_performer.cc
@@ -580,14 +580,19 @@
   for (int i = 0; i < operation.src_extents_size(); i++) {
     ssize_t bytes_read_this_iteration = 0;
     const Extent& extent = operation.src_extents(i);
-    TEST_AND_RETURN_FALSE(utils::PReadAll(fd,
-                                          &buf[bytes_read],
-                                          extent.num_blocks() * block_size_,
-                                          extent.start_block() * block_size_,
-                                          &bytes_read_this_iteration));
+    const size_t bytes = extent.num_blocks() * block_size_;
+    if (extent.start_block() == kSparseHole) {
+      bytes_read_this_iteration = bytes;
+      memset(&buf[bytes_read], 0, bytes);
+    } else {
+      TEST_AND_RETURN_FALSE(utils::PReadAll(fd,
+                                            &buf[bytes_read],
+                                            bytes,
+                                            extent.start_block() * block_size_,
+                                            &bytes_read_this_iteration));
+    }
     TEST_AND_RETURN_FALSE(
-        bytes_read_this_iteration ==
-        static_cast<ssize_t>(extent.num_blocks() * block_size_));
+        bytes_read_this_iteration == static_cast<ssize_t>(bytes));
     bytes_read += bytes_read_this_iteration;
   }
 
@@ -603,11 +608,19 @@
   ssize_t bytes_written = 0;
   for (int i = 0; i < operation.dst_extents_size(); i++) {
     const Extent& extent = operation.dst_extents(i);
-    TEST_AND_RETURN_FALSE(utils::PWriteAll(fd,
-                                           &buf[bytes_written],
-                                           extent.num_blocks() * block_size_,
-                                           extent.start_block() * block_size_));
-    bytes_written += extent.num_blocks() * block_size_;
+    const size_t bytes = extent.num_blocks() * block_size_;
+    if (extent.start_block() == kSparseHole) {
+      DCHECK_EQ(&buf[bytes_written],
+                std::search_n(&buf[bytes_written], &buf[bytes_written + bytes],
+                              bytes, 0));
+    } else {
+      TEST_AND_RETURN_FALSE(
+          utils::PWriteAll(fd,
+                           &buf[bytes_written],
+                           bytes,
+                           extent.start_block() * block_size_));
+    }
+    bytes_written += bytes;
   }
   DCHECK_EQ(bytes_written, bytes_read);
   DCHECK_EQ(bytes_written, static_cast<ssize_t>(buf.size()));
diff --git a/delta_performer_unittest.cc b/delta_performer_unittest.cc
index 0c2c588..83f3863 100644
--- a/delta_performer_unittest.cc
+++ b/delta_performer_unittest.cc
@@ -285,6 +285,20 @@
                                  &hardtocompress[0],
                                  hardtocompress.size()));
 
+    vector<char> zeros(16 * 1024, 0);
+    EXPECT_EQ(zeros.size(),
+              file_util::WriteFile(
+                  FilePath(StringPrintf("%s/move-to-sparse", a_mnt.c_str())),
+                  &zeros[0], zeros.size()));
+
+    EXPECT_TRUE(
+        WriteSparseFile(StringPrintf("%s/move-from-sparse", a_mnt.c_str()),
+                        16 * 1024));
+
+    EXPECT_EQ(0, system(StringPrintf("dd if=/dev/zero of=%s/move-semi-sparse "
+                                     "bs=1 seek=4096 count=1",
+                                     a_mnt.c_str()).c_str()));
+
     // Write 1 MiB of 0xff to try to catch the case where writing a bsdiff
     // patch fails to zero out the final block.
     vector<char> ones(1024 * 1024, 0xff);
@@ -320,7 +334,22 @@
                                      b_mnt.c_str()).c_str()));
     EXPECT_TRUE(WriteSparseFile(StringPrintf("%s/fullsparse", b_mnt.c_str()),
                                 1024 * 1024));
-    EXPECT_EQ(0, system(StringPrintf("dd if=/dev/zero of=%s/partsparese bs=1 "
+
+    EXPECT_TRUE(
+        WriteSparseFile(StringPrintf("%s/move-to-sparse", b_mnt.c_str()),
+                        16 * 1024));
+
+    vector<char> zeros(16 * 1024, 0);
+    EXPECT_EQ(zeros.size(),
+              file_util::WriteFile(
+                  FilePath(StringPrintf("%s/move-from-sparse", b_mnt.c_str())),
+                  &zeros[0], zeros.size()));
+
+    EXPECT_EQ(0, system(StringPrintf("dd if=/dev/zero of=%s/move-semi-sparse "
+                                     "bs=1 seek=4096 count=1",
+                                     b_mnt.c_str()).c_str()));
+
+    EXPECT_EQ(0, system(StringPrintf("dd if=/dev/zero of=%s/partsparse bs=1 "
                                      "seek=4096 count=1",
                                      b_mnt.c_str()).c_str()));
     EXPECT_EQ(0, system(StringPrintf("cp %s/srchardlink0 %s/tmp && "