diff --git a/Documentation/power/freezing-of-tasks.txt b/Documentation/power/freezing-of-tasks.txt
index ec715cd..6ec291e 100644
--- a/Documentation/power/freezing-of-tasks.txt
+++ b/Documentation/power/freezing-of-tasks.txt
@@ -9,7 +9,7 @@
 
 II. How does it work?
 
-There are four per-task flags used for that, PF_NOFREEZE, PF_FROZEN, TIF_FREEZE
+There are three per-task flags used for that, PF_NOFREEZE, PF_FROZEN
 and PF_FREEZER_SKIP (the last one is auxiliary).  The tasks that have
 PF_NOFREEZE unset (all user space processes and some kernel threads) are
 regarded as 'freezable' and treated in a special way before the system enters a
@@ -17,30 +17,31 @@
 we only consider hibernation, but the description also applies to suspend).
 
 Namely, as the first step of the hibernation procedure the function
-freeze_processes() (defined in kernel/power/process.c) is called.  It executes
-try_to_freeze_tasks() that sets TIF_FREEZE for all of the freezable tasks and
-either wakes them up, if they are kernel threads, or sends fake signals to them,
-if they are user space processes.  A task that has TIF_FREEZE set, should react
-to it by calling the function called __refrigerator() (defined in
-kernel/freezer.c), which sets the task's PF_FROZEN flag, changes its state
-to TASK_UNINTERRUPTIBLE and makes it loop until PF_FROZEN is cleared for it.
-Then, we say that the task is 'frozen' and therefore the set of functions
-handling this mechanism is referred to as 'the freezer' (these functions are
-defined in kernel/power/process.c, kernel/freezer.c & include/linux/freezer.h).
-User space processes are generally frozen before kernel threads.
+freeze_processes() (defined in kernel/power/process.c) is called.  A system-wide
+variable system_freezing_cnt (as opposed to a per-task flag) is used to indicate
+whether the system is to undergo a freezing operation. And freeze_processes()
+sets this variable.  After this, it executes try_to_freeze_tasks() that sends a
+fake signal to all user space processes, and wakes up all the kernel threads.
+All freezable tasks must react to that by calling try_to_freeze(), which
+results in a call to __refrigerator() (defined in kernel/freezer.c), which sets
+the task's PF_FROZEN flag, changes its state to TASK_UNINTERRUPTIBLE and makes
+it loop until PF_FROZEN is cleared for it. Then, we say that the task is
+'frozen' and therefore the set of functions handling this mechanism is referred
+to as 'the freezer' (these functions are defined in kernel/power/process.c,
+kernel/freezer.c & include/linux/freezer.h). User space processes are generally
+frozen before kernel threads.
 
 __refrigerator() must not be called directly.  Instead, use the
 try_to_freeze() function (defined in include/linux/freezer.h), that checks
-the task's TIF_FREEZE flag and makes the task enter __refrigerator() if the
-flag is set.
+if the task is to be frozen and makes the task enter __refrigerator().
 
 For user space processes try_to_freeze() is called automatically from the
 signal-handling code, but the freezable kernel threads need to call it
 explicitly in suitable places or use the wait_event_freezable() or
 wait_event_freezable_timeout() macros (defined in include/linux/freezer.h)
-that combine interruptible sleep with checking if TIF_FREEZE is set and calling
-try_to_freeze().  The main loop of a freezable kernel thread may look like the
-following one:
+that combine interruptible sleep with checking if the task is to be frozen and
+calling try_to_freeze().  The main loop of a freezable kernel thread may look
+like the following one:
 
 	set_freezable();
 	do {
@@ -53,7 +54,7 @@
 (from drivers/usb/core/hub.c::hub_thread()).
 
 If a freezable kernel thread fails to call try_to_freeze() after the freezer has
-set TIF_FREEZE for it, the freezing of tasks will fail and the entire
+initiated a freezing operation, the freezing of tasks will fail and the entire
 hibernation operation will be cancelled.  For this reason, freezable kernel
 threads must call try_to_freeze() somewhere or use one of the
 wait_event_freezable() and wait_event_freezable_timeout() macros.
diff --git a/kernel/power/swap.c b/kernel/power/swap.c
index 8742fd0..eef311a 100644
--- a/kernel/power/swap.c
+++ b/kernel/power/swap.c
@@ -51,6 +51,23 @@
 
 #define MAP_PAGE_ENTRIES	(PAGE_SIZE / sizeof(sector_t) - 1)
 
+/*
+ * Number of free pages that are not high.
+ */
+static inline unsigned long low_free_pages(void)
+{
+	return nr_free_pages() - nr_free_highpages();
+}
+
+/*
+ * Number of pages required to be kept free while writing the image. Always
+ * half of all available low pages before the writing starts.
+ */
+static inline unsigned long reqd_free_pages(void)
+{
+	return low_free_pages() / 2;
+}
+
 struct swap_map_page {
 	sector_t entries[MAP_PAGE_ENTRIES];
 	sector_t next_swap;
@@ -72,7 +89,7 @@
 	sector_t cur_swap;
 	sector_t first_sector;
 	unsigned int k;
-	unsigned long nr_free_pages, written;
+	unsigned long reqd_free_pages;
 	u32 crc32;
 };
 
@@ -316,8 +333,7 @@
 		goto err_rel;
 	}
 	handle->k = 0;
-	handle->nr_free_pages = nr_free_pages() >> 1;
-	handle->written = 0;
+	handle->reqd_free_pages = reqd_free_pages();
 	handle->first_sector = handle->cur_swap;
 	return 0;
 err_rel:
@@ -352,11 +368,11 @@
 		handle->cur_swap = offset;
 		handle->k = 0;
 	}
-	if (bio_chain && ++handle->written > handle->nr_free_pages) {
+	if (bio_chain && low_free_pages() <= handle->reqd_free_pages) {
 		error = hib_wait_on_bio_chain(bio_chain);
 		if (error)
 			goto out;
-		handle->written = 0;
+		handle->reqd_free_pages = reqd_free_pages();
 	}
  out:
 	return error;
@@ -618,7 +634,7 @@
 	 * Adjust number of free pages after all allocations have been done.
 	 * We don't want to run out of pages when writing.
 	 */
-	handle->nr_free_pages = nr_free_pages() >> 1;
+	handle->reqd_free_pages = reqd_free_pages();
 
 	/*
 	 * Start the CRC32 thread.