diff --git a/block/io.c b/block/io.c
index 8ca9d43724..0f15d05297 100644
--- a/block/io.c
+++ b/block/io.c
@@ -2368,19 +2368,21 @@ int coroutine_fn bdrv_co_discard(BlockDriverState *bs, int64_t sector_num,
         goto out;
     }
 
-    max_discard = MIN_NON_ZERO(bs->bl.max_discard, BDRV_REQUEST_MAX_SECTORS);
+    max_discard = MIN_NON_ZERO(bs->bl.max_pdiscard >> BDRV_SECTOR_BITS,
+                               BDRV_REQUEST_MAX_SECTORS);
     while (nb_sectors > 0) {
         int ret;
         int num = nb_sectors;
+        int discard_alignment = bs->bl.pdiscard_alignment >> BDRV_SECTOR_BITS;
 
         /* align request */
-        if (bs->bl.discard_alignment &&
-            num >= bs->bl.discard_alignment &&
-            sector_num % bs->bl.discard_alignment) {
-            if (num > bs->bl.discard_alignment) {
-                num = bs->bl.discard_alignment;
+        if (discard_alignment &&
+            num >= discard_alignment &&
+            sector_num % discard_alignment) {
+            if (num > discard_alignment) {
+                num = discard_alignment;
             }
-            num -= sector_num % bs->bl.discard_alignment;
+            num -= sector_num % discard_alignment;
         }
 
         /* limit request size */
diff --git a/block/iscsi.c b/block/iscsi.c
index bde4a04a74..342f6b8186 100644
--- a/block/iscsi.c
+++ b/block/iscsi.c
@@ -1697,13 +1697,6 @@ static void iscsi_close(BlockDriverState *bs)
     memset(iscsilun, 0, sizeof(IscsiLun));
 }
 
-static int sector_limits_lun2qemu(int64_t sector, IscsiLun *iscsilun)
-{
-    int limit = MIN(sector_lun2qemu(sector, iscsilun), INT_MAX / 2 + 1);
-
-    return limit < BDRV_REQUEST_MAX_SECTORS ? limit : 0;
-}
-
 static void iscsi_refresh_limits(BlockDriverState *bs, Error **errp)
 {
     /* We don't actually refresh here, but just return data queried in
@@ -1723,14 +1716,14 @@ static void iscsi_refresh_limits(BlockDriverState *bs, Error **errp)
     }
 
     if (iscsilun->lbp.lbpu) {
-        if (iscsilun->bl.max_unmap < 0xffffffff) {
-            bs->bl.max_discard =
-                sector_limits_lun2qemu(iscsilun->bl.max_unmap, iscsilun);
+        if (iscsilun->bl.max_unmap < 0xffffffff / iscsilun->block_size) {
+            bs->bl.max_pdiscard =
+                iscsilun->bl.max_unmap * iscsilun->block_size;
         }
-        bs->bl.discard_alignment =
-            sector_limits_lun2qemu(iscsilun->bl.opt_unmap_gran, iscsilun);
+        bs->bl.pdiscard_alignment =
+            iscsilun->bl.opt_unmap_gran * iscsilun->block_size;
     } else {
-        bs->bl.discard_alignment = iscsilun->block_size >> BDRV_SECTOR_BITS;
+        bs->bl.pdiscard_alignment = iscsilun->block_size;
     }
 
     if (iscsilun->bl.max_ws_len < 0xffffffff / iscsilun->block_size) {
diff --git a/block/nbd.c b/block/nbd.c
index f5511ea1d4..08e5b67b2f 100644
--- a/block/nbd.c
+++ b/block/nbd.c
@@ -362,7 +362,7 @@ static int nbd_co_flush(BlockDriverState *bs)
 
 static void nbd_refresh_limits(BlockDriverState *bs, Error **errp)
 {
-    bs->bl.max_discard = NBD_MAX_SECTORS;
+    bs->bl.max_pdiscard = NBD_MAX_BUFFER_SIZE;
     bs->bl.max_transfer = NBD_MAX_BUFFER_SIZE;
 }
 
diff --git a/include/block/block_int.h b/include/block/block_int.h
index 7a4a00fdfc..a3e69fd93a 100644
--- a/include/block/block_int.h
+++ b/include/block/block_int.h
@@ -324,11 +324,17 @@ struct BlockDriver {
 };
 
 typedef struct BlockLimits {
-    /* maximum number of sectors that can be discarded at once */
-    int max_discard;
+    /* maximum number of bytes that can be discarded at once (since it
+     * is signed, it must be < 2G, if set), should be multiple of
+     * pdiscard_alignment, but need not be power of 2. May be 0 if no
+     * inherent 32-bit limit */
+    int32_t max_pdiscard;
 
-    /* optimal alignment for discard requests in sectors */
-    int64_t discard_alignment;
+    /* optimal alignment for discard requests in bytes, must be power
+     * of 2, less than max_pdiscard if that is set, and multiple of
+     * bs->request_alignment. May be 0 if bs->request_alignment is
+     * good enough */
+    uint32_t pdiscard_alignment;
 
     /* maximum number of bytes that can zeroized at once (since it is
      * signed, it must be < 2G, if set), should be multiple of
diff --git a/qemu-img.c b/qemu-img.c
index 046b267420..3a7c162fb0 100644
--- a/qemu-img.c
+++ b/qemu-img.c
@@ -2091,7 +2091,8 @@ static int img_convert(int argc, char **argv)
     bufsectors = MIN(32768,
                      MAX(bufsectors,
                          MAX(out_bs->bl.opt_transfer >> BDRV_SECTOR_BITS,
-                             out_bs->bl.discard_alignment)));
+                             out_bs->bl.pdiscard_alignment >>
+                             BDRV_SECTOR_BITS)));
 
     if (skip_create) {
         int64_t output_sectors = blk_nb_sectors(out_blk);