diff --git a/src/sage/rings/number_field/number_field.py b/src/sage/rings/number_field/number_field.py
index a24552a0c6f..ec2717b912e 100644
--- a/src/sage/rings/number_field/number_field.py
+++ b/src/sage/rings/number_field/number_field.py
@@ -12522,7 +12522,7 @@ def map_Zmstar_to_Zm(h):
             p = u.lift()
             while not p.is_prime():
                 p += m
-            f = R.ideal(p).prime_factors()[0].residue_class_degree()
+            f = K.fractional_ideal(p).prime_factors()[0].residue_class_degree()
             h = g**f
             if h not in H:
                 Hgens += [h]
diff --git a/src/sage/rings/number_field/number_field_element.pyx b/src/sage/rings/number_field/number_field_element.pyx
index 30f9c8ba57f..5f166a8c0a4 100644
--- a/src/sage/rings/number_field/number_field_element.pyx
+++ b/src/sage/rings/number_field/number_field_element.pyx
@@ -169,9 +169,8 @@ def _inverse_mod_generic(elt, I):
     """
     from sage.matrix.constructor import matrix
     R = elt.parent()
-    try:
-        I = R.ideal(I)
-    except ValueError:
+    I = R.number_field().fractional_ideal(I)
+    if not I.is_integral():
         raise ValueError("inverse is only defined modulo integral ideals")
     if I == 0:
         raise ValueError("inverse is not defined modulo the zero ideal")
@@ -1984,6 +1983,9 @@ cdef class NumberFieldElement(FieldElement):
             raise ArithmeticError("factorization of 0 is not defined")
 
         K = self.parent()
+        from .order import is_NumberFieldOrder
+        if is_NumberFieldOrder(K):
+            K = K.number_field()
         fac = K.ideal(self).factor()
         # Check whether all prime ideals in `fac` are principal
         for P,e in fac:
@@ -2065,7 +2067,8 @@ cdef class NumberFieldElement(FieldElement):
         if not is_NumberFieldOrder(R) or not R.is_maximal():
             raise NotImplementedError("gcd() for %r is not implemented" % R)
 
-        g = R.ideal(self, other).gens_reduced()
+        K = R.number_field()
+        g = K.fractional_ideal(self, other).gens_reduced()
         if len(g) > 1:
             raise ArithmeticError("ideal (%r, %r) is not principal, gcd is not defined" % (self, other) )
 
diff --git a/src/sage/rings/number_field/order.py b/src/sage/rings/number_field/order.py
index 22f838a9781..4accc937f8e 100644
--- a/src/sage/rings/number_field/order.py
+++ b/src/sage/rings/number_field/order.py
@@ -491,6 +491,14 @@ def ideal(self, *args, **kwds):
         """
         if not self.is_maximal():
             raise NotImplementedError("ideals of non-maximal orders not yet supported.")
+        from sage.misc.superseded import deprecation
+        deprecation(34806, 'In the future, constructing an ideal of the ring of '
+                           'integers of a number field will use an implementation '
+                           'compatible with ideals of other (non-maximal) orders, '
+                           'rather than returning an integral fractional ideal of '
+                           'its containing number field. Use .fractional_ideal(), '
+                           'together with an .is_integral() check if desired, to '
+                           'avoid your code breaking with future changes to Sage.')
         I = self.number_field().ideal(*args, **kwds)
         if not I.is_integral():
             raise ValueError("ideal must be integral; use fractional_ideal to create a non-integral ideal.")