diff --git a/dace/transformation/passes/map_over_free_tasklet.py b/dace/transformation/passes/map_over_free_tasklet.py
index 4756c51263..0c66a90a4e 100644
--- a/dace/transformation/passes/map_over_free_tasklet.py
+++ b/dace/transformation/passes/map_over_free_tasklet.py
@@ -52,10 +52,17 @@ def apply_pass(self, sdfg: SDFG, _: Dict[str, Any]):
                 if isinstance(node, dace.nodes.NestedSDFG):
                     inner_sdfg = node.sdfg
                     self.apply_pass(inner_sdfg, {})
-                elif len(state.in_edges(node)) == 0 and sd[node] is None:
-                    _, start_nodes, end_nodes = self._get_component(state, node)
-                    self._apply(state, start_nodes, end_nodes, counter)
-                    counter += 1
+                elif (len(state.in_edges(node)) == 0
+                      and sd[node] is None
+                      and not isinstance(node, dace.nodes.EntryNode)
+                      and not isinstance(node, dace.nodes.ExitNode)
+                    ):
+                    component, start_nodes, end_nodes = self._get_component(state, node)
+                    # Only apply if there are no entry nodes in the component
+                    has_entry_node = any([isinstance(v, dace.nodes.EntryNode) for v in component])
+                    if not has_entry_node:
+                        self._apply(state, start_nodes, end_nodes, counter)
+                        counter += 1
 
     def _apply(self, state: SDFGState,
                start_nodes: List[dace.nodes.Node],
diff --git a/tests/map_over_free_tasklet_test.py b/tests/map_over_free_tasklet_test.py
index a3fe8a5eaa..d0f086d101 100644
--- a/tests/map_over_free_tasklet_test.py
+++ b/tests/map_over_free_tasklet_test.py
@@ -53,6 +53,48 @@ def _add_chain(
 
     return chain_elements
 
+def _trivial_map_sdfg():
+    sdfg = dace.SDFG("main")
+    state = sdfg.add_state("_s")
+    arr_name, arr = sdfg.add_array("A", (5,), dace.dtypes.float32)
+    an = state.add_access(arr_name)
+    map_entry, map_exit = state.add_map(name="assign", ndrange={
+        "i":dace.subsets.Range([(0, 4, 1)])
+    })
+    t1 = state.add_tasklet("t1", {}, {"_out"}, "_out = 2.0")
+    map_exit.add_in_connector(f"IN_{arr_name}")
+    map_exit.add_out_connector(f"OUT_{arr_name}")
+
+    state.add_edge(map_entry, None, t1, None, dace.memlet.Memlet(None))
+    state.add_edge(t1, "_out", map_exit, f"IN_{arr_name}", dace.memlet.Memlet("A[i]"))
+    state.add_edge(map_exit, f"OUT_{arr_name}", an, None, dace.memlet.Memlet("A[0:5]"))
+
+    sdfg.validate()
+    return sdfg
+
+def _trivial_copy_map_sdfg():
+    sdfg = dace.SDFG("main")
+    state = sdfg.add_state("_s")
+    arr_name, arr = sdfg.add_array("A", (5,), dace.dtypes.float32)
+    an = state.add_access(arr_name)
+    pre_an = state.add_access(arr_name)
+    map_entry, map_exit = state.add_map(name="assign", ndrange={
+        "i":dace.subsets.Range([(0, 4, 1)])
+    })
+    t1 = state.add_tasklet("t1", {"_in"}, {"_out"}, "_out = _in * 2.0")
+    map_exit.add_in_connector(f"IN_{arr_name}")
+    map_exit.add_out_connector(f"OUT_{arr_name}")
+    map_entry.add_in_connector(f"IN_{arr_name}")
+    map_entry.add_out_connector(f"OUT_{arr_name}")
+
+    state.add_edge(pre_an, None, map_entry, f"IN_{arr_name}", dace.memlet.Memlet("A[0:5]"))
+    state.add_edge(map_entry, f"OUT_{arr_name}", t1, "_in", dace.memlet.Memlet("A[i]"))
+    state.add_edge(t1, "_out", map_exit, f"IN_{arr_name}", dace.memlet.Memlet("A[i]"))
+    state.add_edge(map_exit, f"OUT_{arr_name}", an, None, dace.memlet.Memlet("A[0:5]"))
+
+    sdfg.validate()
+    return sdfg
+
 def _trivial_chain_sdfg():
     sdfg = dace.SDFG("main")
     state = sdfg.add_state("_s")
@@ -201,9 +243,34 @@ def test_trivial_chain_in_nested_sdfg():
     _check_recursive(sdfg)
     sdfg.validate()
 
+def _count_maps(sdfg):
+    m = 0
+    for state in sdfg.states():
+        for node in state.nodes():
+            if isinstance(node, dace.nodes.NestedSDFG):
+                m += _count_maps(node.sdfg)
+            elif isinstance(node, dace.nodes.MapEntry):
+                m += 1
+    return m
+
+def test_trivial_assign_map():
+    sdfg = _trivial_map_sdfg()
+    mapOverFreeTasklet = MapOverFreeTasklet()
+    mapOverFreeTasklet.apply_pass(sdfg, {})
+    assert(_count_maps(sdfg) == 1)
+
+def test_trivial_copy_map():
+    sdfg = _trivial_copy_map_sdfg()
+    mapOverFreeTasklet = MapOverFreeTasklet()
+    mapOverFreeTasklet.apply_pass(sdfg, {})
+    assert(_count_maps(sdfg) == 1)
+
+
 if __name__ == "__main__":
     test_trivial_chain()
     test_two_trivial_chains_sdfg()
     test_multiple_input_chain_sdfg()
     test_complex_chain_sdfg()
     test_trivial_chain_in_nested_sdfg()
+    test_trivial_assign_map()
+    test_trivial_copy_map()