diff --git a/src/flint/flint_base/flint_base.pyi b/src/flint/flint_base/flint_base.pyi
index 760baa41..df189363 100644
--- a/src/flint/flint_base/flint_base.pyi
+++ b/src/flint/flint_base/flint_base.pyi
@@ -173,7 +173,7 @@ class flint_mpoly_context(flint_elem, Generic[Tmpoly, Telem, Telem_coerce]):
     def from_dict(self, d: Mapping[tuple[int, ...], Telem_coerce], /) -> Tmpoly: ...
     def constant(self, z: Telem_coerce, /) -> Tmpoly: ...
     def name(self, i: int, /) -> str: ...
-    def names(self) -> tuple[str]: ...
+    def names(self) -> tuple[str, ...]: ...
     def gens(self) -> tuple[Tmpoly, ...]: ...
     def variable_to_index(self, var: str, /) -> int: ...
     def term(
diff --git a/src/flint/flint_base/flint_base.pyx b/src/flint/flint_base/flint_base.pyx
index caf6e8ef..375486dc 100644
--- a/src/flint/flint_base/flint_base.pyx
+++ b/src/flint/flint_base/flint_base.pyx
@@ -959,7 +959,7 @@ cdef class flint_mpoly(flint_elem):
             ('x0', 'x3')
         """
         names = self.context().names()
-        return tuple(names[i] for i, x in enumerate(self.degrees()) if not x)
+        return tuple(names[i] for i, x in enumerate(self.degrees()) if x <= 0)
 
     def project_to_context(self, other_ctx, mapping: dict[str | int, str | int] = None):
         """
diff --git a/src/flint/test/test_all.py b/src/flint/test/test_all.py
index 4f32b8d4..d2f92a1f 100644
--- a/src/flint/test/test_all.py
+++ b/src/flint/test/test_all.py
@@ -3267,6 +3267,8 @@ def quick_poly():
         )
     new_poly = quick_poly().project_to_context(ctx1)
     assert ctx1.drop_gens(new_poly.unused_gens()) == ctx
+    assert quick_poly().unused_gens() == ()
+    assert (0*quick_poly()).unused_gens() == ('x0', 'x1')
     assert new_poly.project_to_context(ctx) == quick_poly()
 
     new_poly = quick_poly().project_to_context(ctx2)
diff --git a/src/flint/types/fmpq_mpoly.pyi b/src/flint/types/fmpq_mpoly.pyi
index 58b388b1..6dec549b 100644
--- a/src/flint/types/fmpq_mpoly.pyi
+++ b/src/flint/types/fmpq_mpoly.pyi
@@ -24,7 +24,7 @@ class fmpq_mpoly_ctx(flint_mpoly_context[fmpq_mpoly, fmpq, ifmpq]):
     def from_dict(self, d: Mapping[tuple[int, ...], ifmpq], /) -> fmpq_mpoly: ...
     def constant(self, q: ifmpq, /) -> fmpq_mpoly: ...
     def name(self, i: int, /) -> str: ...
-    def names(self) -> tuple[str]: ...
+    def names(self) -> tuple[str, ...]: ...
     def gens(self) -> tuple[fmpq_mpoly, ...]: ...
     def variable_to_index(self, var: str, /) -> int: ...
     def term(
diff --git a/src/flint/types/fmpz_mod_mpoly.pyi b/src/flint/types/fmpz_mod_mpoly.pyi
index 17080081..9f04af4f 100644
--- a/src/flint/types/fmpz_mod_mpoly.pyi
+++ b/src/flint/types/fmpz_mod_mpoly.pyi
@@ -36,7 +36,7 @@ class fmpz_mod_mpoly_ctx(flint_mod_mpoly_context[fmpz_mod_mpoly, fmpz_mod, ifmpz
     def constant(self, z: ifmpz_mod) -> fmpz_mod_mpoly: ...
 
     def name(self, i: int, /) -> str: ...
-    def names(self) -> tuple[str]: ...
+    def names(self) -> tuple[str, ...]: ...
     def gens(self) -> tuple[fmpz_mod_mpoly, ...]: ...
     def variable_to_index(self, var: str, /) -> int: ...
     def term(
diff --git a/src/flint/types/fmpz_mpoly.pyi b/src/flint/types/fmpz_mpoly.pyi
index 91d2a2c7..862aa9fa 100644
--- a/src/flint/types/fmpz_mpoly.pyi
+++ b/src/flint/types/fmpz_mpoly.pyi
@@ -22,7 +22,7 @@ class fmpz_mpoly_ctx(flint_mpoly_context[fmpz_mpoly, fmpz, ifmpz]):
     def from_dict(self, d: Mapping[tuple[int, ...], ifmpz], /) -> fmpz_mpoly: ...
     def constant(self, z: ifmpz, /) -> fmpz_mpoly: ...
     def name(self, i: int, /) -> str: ...
-    def names(self) -> tuple[str]: ...
+    def names(self) -> tuple[str, ...]: ...
     def gens(self) -> tuple[fmpz_mpoly, ...]: ...
     def variable_to_index(self, var: str, /) -> int: ...
     def term(
diff --git a/src/flint/types/nmod_mpoly.pyi b/src/flint/types/nmod_mpoly.pyi
index 43ea7d74..183d045a 100644
--- a/src/flint/types/nmod_mpoly.pyi
+++ b/src/flint/types/nmod_mpoly.pyi
@@ -37,7 +37,7 @@ class nmod_mpoly_ctx(flint_mod_mpoly_context[nmod_mpoly, nmod, inmod]):
     def constant(self, z: inmod) -> nmod_mpoly: ...
 
     def name(self, i: int, /) -> str: ...
-    def names(self) -> tuple[str]: ...
+    def names(self) -> tuple[str, ...]: ...
     def gens(self) -> tuple[nmod_mpoly, ...]: ...
     def variable_to_index(self, var: str, /) -> int: ...
     def term(
diff --git a/src/flint/typing.py b/src/flint/typing.py
index 11c71180..94c4edf3 100644
--- a/src/flint/typing.py
+++ b/src/flint/typing.py
@@ -243,7 +243,7 @@ def gen(self, i: int, /) -> _Tmpoly_p: ...
     def from_dict(self, d: Mapping[tuple[int, ...], _Tscalar_contra | int], /) -> _Tmpoly_p: ...
     def constant(self, z: _Tscalar_contra | int, /) -> _Tmpoly_p: ...
     def name(self, i: int, /) -> str: ...
-    def names(self) -> tuple[str]: ...
+    def names(self) -> tuple[str, ...]: ...
     def gens(self) -> tuple[_Tmpoly_p, ...]: ...
     def variable_to_index(self, var: str, /) -> int: ...
     def term(