diff --git a/petab/v2/core.py b/petab/v2/core.py
index b42083f4..72eaec31 100644
--- a/petab/v2/core.py
+++ b/petab/v2/core.py
@@ -19,6 +19,7 @@
     ConfigDict,
     Field,
     ValidationInfo,
+    field_serializer,
     field_validator,
     model_validator,
 )
@@ -875,10 +876,6 @@ def _validate_estimate_before(cls, v):
         if isinstance(v, bool):
             return v
 
-        # FIXME: grace period for 0/1 values until the test suite was updated
-        if v in [0, 1, "0", "1"]:
-            return bool(int(v))
-
         # TODO: clarify whether extra whitespace is allowed
         if isinstance(v, str):
             v = v.strip().lower()
@@ -891,6 +888,10 @@ def _validate_estimate_before(cls, v):
             f"Invalid value for estimate: {v}. Must be `true` or `false`."
         )
 
+    @field_serializer("estimate")
+    def _serialize_estimate(self, estimate: bool, _info):
+        return str(estimate).lower()
+
     @field_validator("lb", "ub", "nominal_value")
     @classmethod
     def _convert_nan_to_none(cls, v):
diff --git a/petab/v2/petab1to2.py b/petab/v2/petab1to2.py
index d7b6fb68..29107238 100644
--- a/petab/v2/petab1to2.py
+++ b/petab/v2/petab1to2.py
@@ -91,12 +91,20 @@ def petab_files_1to2(yaml_config: Path | str, output_dir: Path | str):
     new_yaml_config = v2.ProblemConfig(**new_yaml_config)
 
     # Update tables
-    # condition tables, observable tables, SBML files, parameter table:
-    #  no changes - just copy
+
+    # parameter table:
+    # * parameter.estimate: int -> bool
+    parameter_df = petab_problem.parameter_df.copy()
+    parameter_df[v1.C.ESTIMATE] = parameter_df[v1.C.ESTIMATE].apply(
+        lambda x: str(bool(int(x))).lower()
+    )
     file = yaml_config[v2.C.PARAMETER_FILE]
-    _copy_file(get_src_path(file), Path(get_dest_path(file)))
+    v2.write_parameter_df(parameter_df, get_dest_path(file))
 
+    # sub-problems
     for problem_config in new_yaml_config.problems:
+        # copy files that don't need conversion
+        #  (models, observables, visualizations)
         for file in chain(
             problem_config.observable_files,
             (model.location for model in problem_config.model_files.values()),
diff --git a/petab/v2/problem.py b/petab/v2/problem.py
index 2b564e0c..b0b76aa9 100644
--- a/petab/v2/problem.py
+++ b/petab/v2/problem.py
@@ -939,7 +939,7 @@ def add_observable(
     def add_parameter(
         self,
         id_: str,
-        estimate: bool | str | int = True,
+        estimate: bool | str = True,
         nominal_value: Number | None = None,
         scale: str = None,
         lb: Number = None,
diff --git a/tests/v2/test_problem.py b/tests/v2/test_problem.py
index 67c47a46..55141ba3 100644
--- a/tests/v2/test_problem.py
+++ b/tests/v2/test_problem.py
@@ -140,13 +140,13 @@ def test_modify_problem():
         check_dtype=False,
     )
 
-    problem.add_parameter("parameter1", 1, 0, lb=1, ub=2)
+    problem.add_parameter("parameter1", True, 0, lb=1, ub=2)
     problem.add_parameter("parameter2", False, 2)
 
     exp_parameter_df = pd.DataFrame(
         data={
             PARAMETER_ID: ["parameter1", "parameter2"],
-            ESTIMATE: [1, 0],
+            ESTIMATE: ["true", "false"],
             NOMINAL_VALUE: [0.0, 2.0],
             LOWER_BOUND: [1.0, np.nan],
             UPPER_BOUND: [2.0, np.nan],