diff --git a/block/io.c b/block/io.c
index 7323f0fb7b..d5493ba349 100644
--- a/block/io.c
+++ b/block/io.c
@@ -1180,10 +1180,11 @@ static int coroutine_fn bdrv_co_do_pwrite_zeroes(BlockDriverState *bs,
     int alignment = MAX(bs->bl.pwrite_zeroes_alignment,
                         bs->bl.request_alignment);
 
-    assert(is_power_of_2(alignment));
-    head = offset & (alignment - 1);
-    tail = (offset + count) & (alignment - 1);
-    max_write_zeroes &= ~(alignment - 1);
+    assert(alignment % bs->bl.request_alignment == 0);
+    head = offset % alignment;
+    tail = (offset + count) % alignment;
+    max_write_zeroes = QEMU_ALIGN_DOWN(max_write_zeroes, alignment);
+    assert(max_write_zeroes >= bs->bl.request_alignment);
 
     while (count > 0 && !ret) {
         int num = count;
@@ -2429,9 +2430,10 @@ int coroutine_fn bdrv_co_pdiscard(BlockDriverState *bs, int64_t offset,
 
     /* Discard is advisory, so ignore any unaligned head or tail */
     align = MAX(bs->bl.pdiscard_alignment, bs->bl.request_alignment);
-    assert(is_power_of_2(align));
-    head = MIN(count, -offset & (align - 1));
+    assert(align % bs->bl.request_alignment == 0);
+    head = offset % align;
     if (head) {
+        head = MIN(count, align - head);
         count -= head;
         offset += head;
     }
@@ -2449,6 +2451,7 @@ int coroutine_fn bdrv_co_pdiscard(BlockDriverState *bs, int64_t offset,
 
     max_pdiscard = QEMU_ALIGN_DOWN(MIN_NON_ZERO(bs->bl.max_pdiscard, INT_MAX),
                                    align);
+    assert(max_pdiscard);
 
     while (count > 0) {
         int ret;
diff --git a/include/block/block_int.h b/include/block/block_int.h
index 1fe0fd9ff6..47665be81e 100644
--- a/include/block/block_int.h
+++ b/include/block/block_int.h
@@ -330,36 +330,39 @@ typedef struct BlockLimits {
      * otherwise. */
     uint32_t request_alignment;
 
-    /* maximum number of bytes that can be discarded at once (since it
-     * is signed, it must be < 2G, if set), should be multiple of
+    /* Maximum number of bytes that can be discarded at once (since it
+     * is signed, it must be < 2G, if set). Must 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 bytes, must be power
-     * of 2, less than max_pdiscard if that is set, and multiple of
-     * bl.request_alignment. May be 0 if bl.request_alignment is good
-     * enough */
+    /* Optimal alignment for discard requests in bytes. A power of 2
+     * is best but not mandatory.  Must be a multiple of
+     * bl.request_alignment, and must be less than max_pdiscard if
+     * that is set. May be 0 if bl.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
+    /* Maximum number of bytes that can zeroized at once (since it is
+     * signed, it must be < 2G, if set). Must be multiple of
      * pwrite_zeroes_alignment. May be 0 if no inherent 32-bit limit */
     int32_t max_pwrite_zeroes;
 
-    /* optimal alignment for write zeroes requests in bytes, must be
-     * power of 2, less than max_pwrite_zeroes if that is set, and
-     * multiple of bl.request_alignment. May be 0 if
-     * bl.request_alignment is good enough */
+    /* Optimal alignment for write zeroes requests in bytes. A power
+     * of 2 is best but not mandatory.  Must be a multiple of
+     * bl.request_alignment, and must be less than max_pwrite_zeroes
+     * if that is set. May be 0 if bl.request_alignment is good
+     * enough */
     uint32_t pwrite_zeroes_alignment;
 
-    /* optimal transfer length in bytes (must be power of 2, and
-     * multiple of bl.request_alignment), or 0 if no preferred size */
+    /* Optimal transfer length in bytes.  A power of 2 is best but not
+     * mandatory.  Must be a multiple of bl.request_alignment, or 0 if
+     * no preferred size */
     uint32_t opt_transfer;
 
-    /* maximal transfer length in bytes (need not be power of 2, but
-     * should be multiple of opt_transfer), or 0 for no 32-bit limit.
-     * For now, anything larger than INT_MAX is clamped down. */
+    /* Maximal transfer length in bytes.  Need not be power of 2, but
+     * must be multiple of opt_transfer and bl.request_alignment, or 0
+     * for no 32-bit limit.  For now, anything larger than INT_MAX is
+     * clamped down. */
     uint32_t max_transfer;
 
     /* memory alignment, in bytes so that no bounce buffer is needed */