diff --git a/src/sage/combinat/boltzmann_sampling/generator.pyx b/src/sage/combinat/boltzmann_sampling/generator.pyx
index e5ffbb707ec..61a1f799f58 100644
--- a/src/sage/combinat/boltzmann_sampling/generator.pyx
+++ b/src/sage/combinat/boltzmann_sampling/generator.pyx
@@ -80,7 +80,7 @@ from functools import reduce
 
 from sage.libs.gmp.random cimport gmp_randinit_set, gmp_randinit_default
 from sage.libs.gmp.types cimport gmp_randstate_t
-from sage.misc.randstate cimport randstate, current_randstate
+from sage.misc.randstate cimport randstate, current_randstate, SAGE_RAND_MAX
 
 from .grammar import Atom, Product, Ref, Union
 from .oracle import SimpleOracle, find_singularity
@@ -231,6 +231,70 @@ cdef c_generate(first_rule, rules, builders, randstate rstate):
     obj, = generated
     return obj
 
+cdef int rand_int(int bound, randstate rstate):
+    r = rstate.c_random()
+    v = r % bound
+    if r - v > SAGE_RAND_MAX - bound + 1:
+        return rand_int(bound, rstate)
+    else:
+        return v
+
+cdef select(int r, sizes):
+    r = r
+    for i in range(len(sizes)):
+        r -= sizes[i]
+        if r < 0:
+            sizes[i] -= 1
+            return i
+
+cdef shuffle(bag, sizes, total_size, rstate):
+    total_size = total_size
+    bags = [[] for __ in sizes]
+    for total_size in range(total_size, 0, -1):
+        r = rand_int(total_size, rstate)
+        i = select(r, sizes)
+        label = bag.pop()
+        bags[i].append(label)
+    return bags
+
+cdef tree_size(tree):
+    __, __, size = tree
+    return size
+
+cdef labelling(tree, builders, randstate rstate):
+    bag = list(range(tree_size(tree)))
+    generated = []
+    todo = [(tree, bag)]
+
+    while todo:
+        (type, content, size), bag = todo.pop()
+        if type == REF:
+            rule_id, children = content
+            todo.append((FUNCTION, rule_id, size))
+            todo.append(children)
+        elif type == ATOM:
+            name = content
+            assert len(bag) == size
+            generated.append((name, bag))
+        elif type == PRODUCT:
+            sizes = [tree_size(t) for t in content]
+            bags = shuffle(bag, sizes, size, rstate)
+            todo.append((TUPLE, len(content), size))
+            for i in range(len(content)):
+                todo.append((content[i], bags[i]))
+        elif type == TUPLE:
+            nargs = content
+            t = tuple(generated[-nargs:])
+            generated = generated[:-nargs]
+            generated.append(t)
+        elif type == FUNCTION:
+            func = builders[content]
+            x = generated.pop()
+            generated.append(func(x))
+
+    tree, = generated
+    return tree
+
 cdef c_gen(first_rule, rules, int size_min, int size_max, int max_retry, builders):
     """Search for a tree in a given size window. Wrapper around c_simulate and
     c_generate."""
@@ -329,6 +393,39 @@ cdef make_default_builder(rule):
         subbuilders = [make_default_builder(component) for component in rule.args]
         return ProductBuilder(subbuilders)
 
+# ---
+# Generic tree builders with size annotations
+# ---
+
+cdef size_ref_builder(id):
+    def build(x):
+        __, __, size = x
+        return (REF, (id, x), size)
+    return build
+
+cdef size_atom_builder(x):
+    name, size = x
+    return (ATOM, name, size)
+
+cdef size_product_builder(builders):
+    def build(terms):
+        t = tuple(builders[i](terms[i]) for i in range(len(terms)))
+        size = sum([s for __, __, s in t])
+        return (PRODUCT, t, size)
+    return build
+
+cdef size_builder(name_to_id, rule):
+    if isinstance(rule, Ref):
+        return size_ref_builder(name_to_id[rule.name])
+    elif isinstance(rule, Atom):
+        return size_atom_builder
+    elif isinstance(rule, Union):
+        subbuilders = [size_builder(name_to_id, component) for component in rule.args]
+        return UnionBuilder(*subbuilders)
+    elif isinstance(rule, Product):
+        subbuilders = [size_builder(name_to_id, component) for component in rule.args]
+        return size_product_builder(subbuilders)
+
 # ---
 # High level interface
 # ---