diff --git a/kernel/power/snapshot.c b/kernel/power/snapshot.c
index 2b1a7bc24c913e29dc772009e339b5682589fdcd..0a06b114dd336ebe49580a1dedfeb33bc4cf5600 100644
--- a/kernel/power/snapshot.c
+++ b/kernel/power/snapshot.c
@@ -1203,6 +1203,36 @@ static void free_unnecessary_pages(void)
 	}
 }
 
+/**
+ * minimum_image_size - Estimate the minimum acceptable size of an image
+ * @saveable: Number of saveable pages in the system.
+ *
+ * We want to avoid attempting to free too much memory too hard, so estimate the
+ * minimum acceptable size of a hibernation image to use as the lower limit for
+ * preallocating memory.
+ *
+ * We assume that the minimum image size should be proportional to
+ *
+ * [number of saveable pages] - [number of pages that can be freed in theory]
+ *
+ * where the second term is the sum of (1) reclaimable slab pages, (2) active
+ * and (3) inactive anonymouns pages, (4) active and (5) inactive file pages,
+ * minus mapped file pages.
+ */
+static unsigned long minimum_image_size(unsigned long saveable)
+{
+	unsigned long size;
+
+	size = global_page_state(NR_SLAB_RECLAIMABLE)
+		+ global_page_state(NR_ACTIVE_ANON)
+		+ global_page_state(NR_INACTIVE_ANON)
+		+ global_page_state(NR_ACTIVE_FILE)
+		+ global_page_state(NR_INACTIVE_FILE)
+		- global_page_state(NR_FILE_MAPPED);
+
+	return saveable <= size ? 0 : saveable - size;
+}
+
 /**
  * hibernate_preallocate_memory - Preallocate memory for hibernation image
  *
@@ -1220,8 +1250,8 @@ static void free_unnecessary_pages(void)
  *
  * If image_size is set below the number following from the above formula,
  * the preallocation of memory is continued until the total number of saveable
- * pages in the system is below the requested image size or it is impossible to
- * allocate more memory, whichever happens first.
+ * pages in the system is below the requested image size or the minimum
+ * acceptable image size returned by minimum_image_size(), whichever is greater.
  */
 int hibernate_preallocate_memory(void)
 {
@@ -1282,6 +1312,11 @@ int hibernate_preallocate_memory(void)
 		goto out;
 	}
 
+	/* Estimate the minimum size of the image. */
+	pages = minimum_image_size(saveable);
+	if (size < pages)
+		size = min_t(unsigned long, pages, max_size);
+
 	/*
 	 * Let the memory management subsystem know that we're going to need a
 	 * large number of page frames to allocate and make it free some memory.
@@ -1294,8 +1329,8 @@ int hibernate_preallocate_memory(void)
 	 * The number of saveable pages in memory was too high, so apply some
 	 * pressure to decrease it.  First, make room for the largest possible
 	 * image and fail if that doesn't work.  Next, try to decrease the size
-	 * of the image as much as indicated by image_size using allocations
-	 * from highmem and non-highmem zones separately.
+	 * of the image as much as indicated by 'size' using allocations from
+	 * highmem and non-highmem zones separately.
 	 */
 	pages_highmem = preallocate_image_highmem(highmem / 2);
 	alloc = (count - max_size) - pages_highmem;