diff --git a/python/sdist/amici/sbml_import.py b/python/sdist/amici/sbml_import.py
index dcff20a3f9..1ac2d6a4cc 100644
--- a/python/sdist/amici/sbml_import.py
+++ b/python/sdist/amici/sbml_import.py
@@ -722,7 +722,7 @@ def _gather_base_locals(
             "INF": sp.oo,
             "NaN": sp.nan,
             "rem": sp.Mod,
-            "time": symbol_with_assumptions("time"),
+            "time": sbml_time_symbol,
             # SBML L3 explicitly defines this value, which is not equal
             # to the most recent SI definition.
             "avogadro": sp.Float(6.02214179e23),
@@ -1096,11 +1096,14 @@ def _process_parameters(
 
         # Parameters that need to be turned into expressions
         #  so far, this concerns parameters with symbolic initial assignments
-        #  (those have been skipped above)
+        #  (those have been skipped above) that are not rate rule targets
         for par in self.sbml.getListOfParameters():
             if (
-                ia := self._get_element_initial_assignment(par.getId())
-            ) is not None and not ia.is_Number:
+                (ia := self._get_element_initial_assignment(par.getId()))
+                is not None
+                and not ia.is_Number
+                and not self.is_rate_rule_target(par)
+            ):
                 self.symbols[SymbolId.EXPRESSION][
                     _get_identifier_symbol(par)
                 ] = {
@@ -1875,7 +1878,9 @@ def _process_initial_assignments(self):
         for ia in self.sbml.getListOfInitialAssignments():
             identifier = _get_identifier_symbol(ia)
             if identifier in itt.chain(
-                self.symbols[SymbolId.SPECIES], self.compartments
+                self.symbols[SymbolId.SPECIES],
+                self.compartments,
+                self.symbols[SymbolId.EXPRESSION],
             ):
                 continue
 
@@ -1949,9 +1954,7 @@ def _make_initial(
             if "init" in species:
                 sym_math = smart_subs(sym_math, species_id, species["init"])
 
-        sym_math = smart_subs(
-            sym_math, self._local_symbols["time"], sp.Float(0)
-        )
+        sym_math = smart_subs(sym_math, sbml_time_symbol, sp.Float(0))
 
         sym_math = _dummy_to_rateof(sym_math, rateof_to_dummy)