diff --git a/Memory-Manager.md b/Memory-Manager.md
index 310b98d..6b09c90 100644
--- a/Memory-Manager.md
+++ b/Memory-Manager.md
@@ -89,9 +89,6 @@ def gc_collect(): # implemented by ports
   # add root pointers (platform-dependent)
   gc_collect_root(roots)
 
-  # mark all reachable blocks
-  gc_mark()
-
   # if there was a stack overflow, scan all memory for reachable blocks
   gc_deal_with_stack_overflow()
 
@@ -100,41 +97,48 @@ def gc_collect(): # implemented by ports
 
 def gc_collect_root(roots):
   for root in roots:
-    # Add this root to the (empty) stack. len(gc.stack) will be 1.
-    may_add_to_stack(root)
+    # Test whether this could be a pointer.
+    if looks_like_pointer(root):
+      block = block_from_ptr(root)
+      if block.state == HEAD:
+        # Set the mark bit on this block.
+        block.state = MARK
 
-    # Shrink the stack to zero, hopefully without GC stack overflow.
-    gc_drain_stack()
+        # Mark all descendants of this root.
+        gc_mark_subtree(block)
 
-def may_add_to_stack(pointer): # VERIFY_MARK_AND_PUSH
-  # If this is a pointer and points to an unmarked block, mark it and try to
-  # push it on the stack.
-  if is_heap_pointer(pointer):
-    # Get the block number this pointer points to.
-    block = BLOCK_FROM_PTR(pointer)
-    if block.state == HEAD:
-      block.state = MARK
-      # Is there space left on the GC stack?
-      if len(gc.stack) < MICROPY_ALLOC_GC_STACK_SIZE:
-        # Yes, add this block to the stack.
-        gc.stack.append(block)
-      else:
-        # Sadly, no. The mark phase can continue, but the whole memory will need
-        # to be scanned again (some marked blocks may have unmarked children).
-        gc.stack_overflow = True
+def gc_mark_subtree(block):
+  # The passed in block must already been marked.
 
-def gc_drain_stack():
   # Try to reduce the stack, and don't return until it's empty. But with every
   # reduction, multiple blocks may be added to the stack so this function may
   # actually hit a stack overflow.
-  while len(gc.stack) > 0:
-    block = gc.stack.pop()
+  while True:
+    # Check this block's children.
     # Each block contains 4 memory words (on a 32-bit system with 16-byte
     # blocks). These words may be pointers to blocks on the heap, but may also
     # be other things like integers, parts of raw data (strings, bytecode, etc.)
     # or pointers to memory outside of the heap.
-    for pointer in block:
-      may_add_to_stack(pointer)
+    for pointer in reversed(block.all_pointers_in_chain()[1:]):
+      if looks_like_pointer(pointer):
+        childblock = block_from_ptr(pointer)
+        if childblock.state == HEAD:
+          childblock.state = MARK
+          # Is there space left on the GC stack?
+          if len(gc.stack) < MICROPY_ALLOC_GC_STACK_SIZE:
+            # Yes, add this block to the stack.
+            gc.stack.append(block)
+          else:
+            # Sadly, no. The mark phase can continue, but the whole memory will need
+            # to be scanned again (some marked blocks may have unmarked children).
+            gc.stack_overflow = True
+
+    # Are there any blocks on the stack?
+    if len(gc.stack) == 0:
+      break # No, stack is empty, we're done.
+
+    # pop the next block off the stack
+    block = gc.stack.pop()
 
 def gc_deal_with_stack_overflow():
   # Keep scanning the whole memory until all marked blocks don't have unmarked
@@ -143,16 +147,13 @@ def gc_deal_with_stack_overflow():
   # The stack is there to make the mark phase more efficient, i.e. it avoids
   # having to scan the whole memory too often. But sometimes, the stack is too
   # small and requires a full scan (like at the beginning of the mark phase).
-  gc.stack_overflow = True # indicates the whole memory needs to be scanned
   while gc.stack_overflow:
     gc.stack_overflow = False
-    gc.stack = []
     for block in gc.memory:
       # A block can have the states FREE, HEAD, TAIL or MARK, as set in the
       # allocation table.
       if block.state == MARK:
-        gc.stack.append(block)
-        gc_drain_stack()
+        gc_mark_subtree(block)
 
 def gc_sweep():
   # Free unmarked blocks and unmark marked blocks.