diff --git a/src/sage/sets/disjoint_set.pyx b/src/sage/sets/disjoint_set.pyx
index 7a832104295..ddd9a95a310 100644
--- a/src/sage/sets/disjoint_set.pyx
+++ b/src/sage/sets/disjoint_set.pyx
@@ -62,7 +62,10 @@ from sage.rings.integer cimport Integer
 from sage.structure.sage_object cimport SageObject
 from cpython.object cimport PyObject_RichCompare
 from sage.groups.perm_gps.partn_ref.data_structures cimport *
-from sage.combinat.set_partition import SetPartition
+from sage.misc.lazy_import import LazyImport
+
+SetPartition = LazyImport('sage.combinat.set_partition', 'SetPartition')
+
 
 cpdef DisjointSet(arg):
     r"""
diff --git a/src/sage/sets/image_set.py b/src/sage/sets/image_set.py
index 8691edbcd01..a518dc58f93 100644
--- a/src/sage/sets/image_set.py
+++ b/src/sage/sets/image_set.py
@@ -25,7 +25,6 @@
 from sage.misc.cachefunc import cached_method
 from sage.rings.infinity import Infinity
 from sage.rings.integer import Integer
-from sage.modules.free_module import FreeModule
 from sage.structure.element import Expression
 from sage.structure.parent import Parent
 
@@ -91,6 +90,7 @@ def __init__(self, map, domain_subset, *, category=None, is_injective=None, inve
             if isinstance(map, Expression) and map.is_callable():
                 domain = map.parent().base()
                 if len(map.arguments()) != 1:
+                    from sage.modules.free_module import FreeModule
                     domain = FreeModule(domain, len(map.arguments()))
                 function = map