diff --git a/.github/workflows/buildwheel.yml b/.github/workflows/buildwheel.yml
index 73981d50..12a380e5 100644
--- a/.github/workflows/buildwheel.yml
+++ b/.github/workflows/buildwheel.yml
@@ -179,7 +179,7 @@ jobs:
       fail-fast: false
       matrix:
         # Supported Flint versions:
-        flint-tag: ['v3.0.1', 'v3.1.3-p1', 'v3.2.2']
+        flint-tag: ['v3.0.1', 'v3.1.3-p1', 'v3.2.2', 'v3.3.1']
     steps:
       - uses: actions/checkout@v4
       - uses: actions/setup-python@v5
diff --git a/src/flint/test/test_all.py b/src/flint/test/test_all.py
index f38f1b35..59d1c46a 100644
--- a/src/flint/test/test_all.py
+++ b/src/flint/test/test_all.py
@@ -696,6 +696,12 @@ def test_fmpz_series():
     assert s1._equal_repr(1) is False
     assert Z([])._equal_repr(Z([0])) is True
     assert Z([1])._equal_repr(Z([0])) is False
+    p = Z([1,2])
+    assert p.prec == 10
+    p4 = Z([1,2], prec=4)
+    assert p4.prec == 4
+    p4 = Z(p, prec=4)
+    assert p4.prec == 4
     # XXX: this gives a core dump:
     # s = Z([1,2])
     # s[10**10] = 1
@@ -1200,6 +1206,12 @@ def test_fmpq_series():
     assert s1._equal_repr(sz3) is False
     assert Q([1])._equal_repr(flint.fmpq(1)) is False
     assert Q([1])._equal_repr(1) is False
+    p = Q([1,2])
+    assert p.prec == 10
+    p4 = Q([1,2], prec=4)
+    assert p4.prec == 4
+    p4 = Q(p, prec=4)
+    assert p4.prec == 4
     # XXX: this gives a core dump:
     # s = Q([1,2])
     # s[10**10] = 1
diff --git a/src/flint/types/fmpq_series.pyx b/src/flint/types/fmpq_series.pyx
index 1ce75c10..a99f530c 100644
--- a/src/flint/types/fmpq_series.pyx
+++ b/src/flint/types/fmpq_series.pyx
@@ -75,10 +75,10 @@ cdef class fmpq_series(flint_series):
         if val is not None:
             if typecheck(val, fmpq_series):
                 fmpq_poly_set(self.val, (<fmpq_series>val).val)
-                self._prec = min((<fmpq_series>val)._prec, getcap())
+                self._prec = min((<fmpq_series>val)._prec, self._prec)
             elif typecheck(val, fmpz_series):
                 fmpq_poly_set_fmpz_poly(self.val, (<fmpz_series>val).val)
-                self._prec = min((<fmpz_series>val)._prec, getcap())
+                self._prec = min((<fmpz_series>val)._prec, self._prec)
             elif typecheck(val, fmpz_poly):
                 fmpq_poly_set_fmpz_poly(self.val, (<fmpz_poly>val).val)
             elif typecheck(val, fmpq_poly):
diff --git a/src/flint/types/fmpz_series.pyx b/src/flint/types/fmpz_series.pyx
index 06ff936d..07bc519d 100644
--- a/src/flint/types/fmpz_series.pyx
+++ b/src/flint/types/fmpz_series.pyx
@@ -68,7 +68,7 @@ cdef class fmpz_series(flint_series):
         if val is not None:
             if typecheck(val, fmpz_series):
                 fmpz_poly_set(self.val, (<fmpz_series>val).val)
-                self._prec = min((<fmpz_series>val)._prec, getcap())
+                self._prec = min((<fmpz_series>val)._prec, self._prec)
             elif typecheck(val, fmpz_poly):
                 fmpz_poly_set(self.val, (<fmpz_poly>val).val)
             elif typecheck(val, list):