diff --git a/src/optimagic/optimization/algorithm.py b/src/optimagic/optimization/algorithm.py
index 7f776cf90..c52245c4f 100644
--- a/src/optimagic/optimization/algorithm.py
+++ b/src/optimagic/optimization/algorithm.py
@@ -10,12 +10,16 @@
 
 from optimagic.exceptions import InvalidAlgoInfoError, InvalidAlgoOptionError
 from optimagic.logging.types import StepStatus
+from optimagic.optimization.convergence_report import get_convergence_report
 from optimagic.optimization.history import History
 from optimagic.optimization.internal_optimization_problem import (
     InternalOptimizationProblem,
 )
+from optimagic.optimization.optimize_result import OptimizeResult
+from optimagic.parameters.conversion import Converter
 from optimagic.type_conversion import TYPE_CONVERTERS
-from optimagic.typing import AggregationLevel
+from optimagic.typing import AggregationLevel, Direction, ExtraResultFields
+from optimagic.utilities import isscalar
 
 
 @dataclass(frozen=True)
@@ -142,6 +146,56 @@ def __post_init__(self) -> None:
             )
             raise TypeError(msg)
 
+    def create_optimize_result(
+        self,
+        converter: Converter,
+        solver_type: AggregationLevel,
+        extra_fields: ExtraResultFields,
+    ) -> OptimizeResult:
+        """Process an internal optimizer result."""
+        params = converter.params_from_internal(self.x)
+        if isscalar(self.fun):
+            fun = float(self.fun)
+        elif solver_type == AggregationLevel.LIKELIHOOD:
+            fun = float(np.sum(self.fun))
+        elif solver_type == AggregationLevel.LEAST_SQUARES:
+            fun = np.dot(self.fun, self.fun)
+
+        if extra_fields.direction == Direction.MAXIMIZE:
+            fun = -fun
+
+        if self.history is not None:
+            conv_report = get_convergence_report(
+                history=self.history, direction=extra_fields.direction
+            )
+        else:
+            conv_report = None
+
+        out = OptimizeResult(
+            params=params,
+            fun=fun,
+            start_fun=extra_fields.start_fun,
+            start_params=extra_fields.start_params,
+            algorithm=extra_fields.algorithm,
+            direction=extra_fields.direction.value,
+            n_free=extra_fields.n_free,
+            message=self.message,
+            success=self.success,
+            n_fun_evals=self.n_fun_evals,
+            n_jac_evals=self.n_jac_evals,
+            n_hess_evals=self.n_hess_evals,
+            n_iterations=self.n_iterations,
+            status=self.status,
+            jac=self.jac,
+            hess=self.hess,
+            hess_inv=self.hess_inv,
+            max_constraint_violation=self.max_constraint_violation,
+            history=self.history,
+            algorithm_output=self.info,
+            convergence_report=conv_report,
+        )
+        return out
+
 
 class AlgorithmMeta(ABCMeta):
     """Metaclass to get repr, algo_info and name for classes, not just instances."""
@@ -234,7 +288,7 @@ def solve_internal_problem(
         problem: InternalOptimizationProblem,
         x0: NDArray[np.float64],
         step_id: int,
-    ) -> InternalOptimizeResult:
+    ) -> OptimizeResult:
         problem = problem.with_new_history().with_step_id(step_id)
 
         if problem.logger:
@@ -242,17 +296,23 @@ def solve_internal_problem(
                 step_id, {"status": str(StepStatus.RUNNING.value)}
             )
 
-        result = self._solve_internal_problem(problem, x0)
+        raw_res = self._solve_internal_problem(problem, x0)
 
-        if (not self.algo_info.disable_history) and (result.history is None):
-            result = replace(result, history=problem.history)
+        if (not self.algo_info.disable_history) and (raw_res.history is None):
+            raw_res = replace(raw_res, history=problem.history)
 
         if problem.logger:
             problem.logger.step_store.update(
                 step_id, {"status": str(StepStatus.COMPLETE.value)}
             )
 
-        return result
+        res = raw_res.create_optimize_result(
+            converter=problem.converter,
+            solver_type=self.algo_info.solver_type,
+            extra_fields=problem.static_result_fields,
+        )
+
+        return res
 
     def with_option_if_applicable(self, **kwargs: Any) -> Self:
         """Call with_option only with applicable keyword arguments."""
diff --git a/src/optimagic/optimization/multistart.py b/src/optimagic/optimization/multistart.py
index c3d4cf3e1..c6de25bff 100644
--- a/src/optimagic/optimization/multistart.py
+++ b/src/optimagic/optimization/multistart.py
@@ -12,7 +12,6 @@
 """
 
 import warnings
-from dataclasses import replace
 from typing import Literal
 
 import numpy as np
@@ -21,7 +20,7 @@
 
 from optimagic.logging.logger import LogStore
 from optimagic.logging.types import StepStatus
-from optimagic.optimization.algorithm import Algorithm, InternalOptimizeResult
+from optimagic.optimization.algorithm import Algorithm
 from optimagic.optimization.internal_optimization_problem import (
     InternalBounds,
     InternalOptimizationProblem,
@@ -30,6 +29,8 @@
 from optimagic.optimization.optimization_logging import (
     log_scheduled_steps_and_get_ids,
 )
+from optimagic.optimization.optimize_result import OptimizeResult
+from optimagic.optimization.process_results import process_multistart_result
 from optimagic.typing import AggregationLevel, ErrorHandling
 from optimagic.utilities import get_rng
 
@@ -42,7 +43,7 @@ def run_multistart_optimization(
     options: InternalMultistartOptions,
     logger: LogStore | None,
     error_handling: ErrorHandling,
-) -> InternalOptimizeResult:
+) -> OptimizeResult:
     steps = determine_steps(options.n_samples, stopping_maxopt=options.stopping_maxopt)
 
     scheduled_steps = log_scheduled_steps_and_get_ids(
@@ -159,6 +160,7 @@ def single_optimization(x0, step_id):
             results=batch_results,
             convergence_criteria=convergence_criteria,
             solver_type=local_algorithm.algo_info.solver_type,
+            converter=internal_problem.converter,
         )
         opt_counter += len(batch)
         if is_converged:
@@ -176,7 +178,12 @@ def single_optimization(x0, step_id):
     }
 
     raw_res = state["best_res"]
-    res = replace(raw_res, multistart_info=multistart_info)
+    res = process_multistart_result(
+        raw_res=raw_res,
+        converter=internal_problem.converter,
+        extra_fields=internal_problem.static_result_fields,
+        multistart_info=multistart_info,
+    )
 
     return res
 
@@ -371,7 +378,12 @@ def get_batched_optimization_sample(sorted_sample, stopping_maxopt, batch_size):
 
 
 def update_convergence_state(
-    current_state, starts, results, convergence_criteria, solver_type
+    current_state,
+    starts,
+    results,
+    convergence_criteria,
+    solver_type,
+    converter,
 ):
     """Update the state of all quantities related to convergence.
 
@@ -389,6 +401,7 @@ def update_convergence_state(
         convergence_criteria (dict): Dict with the entries "xtol" and "max_discoveries"
         solver_type: The aggregation level of the local optimizer. Needed to
             interpret the output of the internal criterion function.
+        converter: The converter to map between internal and external parameter spaces.
 
 
     Returns:
@@ -422,7 +435,7 @@ def update_convergence_state(
     # ==================================================================================
     valid_results = [results[i] for i in valid_indices]
     valid_starts = [starts[i] for i in valid_indices]
-    valid_new_x = [res.x for res in valid_results]
+    valid_new_x = [converter.params_to_internal(res.params) for res in valid_results]
     valid_new_y = []
 
     # make the criterion output scalar if a least squares optimizer returns an
diff --git a/src/optimagic/optimization/optimize.py b/src/optimagic/optimization/optimize.py
index fc1cbdeef..5a383ff86 100644
--- a/src/optimagic/optimization/optimize.py
+++ b/src/optimagic/optimization/optimize.py
@@ -48,10 +48,6 @@
 )
 from optimagic.optimization.optimization_logging import log_scheduled_steps_and_get_ids
 from optimagic.optimization.optimize_result import OptimizeResult
-from optimagic.optimization.process_results import (
-    process_multistart_result,
-    process_single_result,
-)
 from optimagic.parameters.bounds import Bounds
 from optimagic.parameters.conversion import (
     get_converter,
@@ -644,7 +640,7 @@ def _optimize(problem: OptimizationProblem) -> OptimizeResult:
             logger=logger,
         )[0]
 
-        raw_res = problem.algorithm.solve_internal_problem(internal_problem, x, step_id)
+        res = problem.algorithm.solve_internal_problem(internal_problem, x, step_id)
 
     else:
         multistart_options = get_internal_multistart_options_from_public(
@@ -658,7 +654,7 @@ def _optimize(problem: OptimizationProblem) -> OptimizeResult:
             upper=internal_params.soft_upper_bounds,
         )
 
-        raw_res = run_multistart_optimization(
+        res = run_multistart_optimization(
             local_algorithm=problem.algorithm,
             internal_problem=internal_problem,
             x=x,
@@ -672,21 +668,6 @@ def _optimize(problem: OptimizationProblem) -> OptimizeResult:
     # Process the result
     # ==================================================================================
 
-    if problem.multistart is None:
-        res = process_single_result(
-            raw_res=raw_res,
-            converter=converter,
-            solver_type=problem.algorithm.algo_info.solver_type,
-            extra_fields=extra_fields,
-        )
-    else:
-        res = process_multistart_result(
-            raw_res=raw_res,
-            converter=converter,
-            solver_type=problem.algorithm.algo_info.solver_type,
-            extra_fields=extra_fields,
-        )
-
     log_reader: LogReader[Any] | None
     if logger is not None:
         assert problem.logging is not None
diff --git a/src/optimagic/optimization/process_results.py b/src/optimagic/optimization/process_results.py
index 2843c7325..890437668 100644
--- a/src/optimagic/optimization/process_results.py
+++ b/src/optimagic/optimization/process_results.py
@@ -1,91 +1,29 @@
-from dataclasses import replace
+import copy
 from typing import Any
 
 import numpy as np
 
-from optimagic.optimization.algorithm import InternalOptimizeResult
 from optimagic.optimization.convergence_report import get_convergence_report
 from optimagic.optimization.optimize_result import MultistartInfo, OptimizeResult
 from optimagic.parameters.conversion import Converter
-from optimagic.typing import AggregationLevel, Direction, ExtraResultFields
-from optimagic.utilities import isscalar
-
-
-def process_single_result(
-    raw_res: InternalOptimizeResult,
-    converter: Converter,
-    solver_type: AggregationLevel,
-    extra_fields: ExtraResultFields,
-) -> OptimizeResult:
-    """Process an internal optimizer result."""
-    params = converter.params_from_internal(raw_res.x)
-    if isscalar(raw_res.fun):
-        fun = float(raw_res.fun)
-    elif solver_type == AggregationLevel.LIKELIHOOD:
-        fun = float(np.sum(raw_res.fun))
-    elif solver_type == AggregationLevel.LEAST_SQUARES:
-        fun = np.dot(raw_res.fun, raw_res.fun)
-
-    if extra_fields.direction == Direction.MAXIMIZE:
-        fun = -fun
-
-    if raw_res.history is not None:
-        conv_report = get_convergence_report(
-            history=raw_res.history, direction=extra_fields.direction
-        )
-    else:
-        conv_report = None
-
-    out = OptimizeResult(
-        params=params,
-        fun=fun,
-        start_fun=extra_fields.start_fun,
-        start_params=extra_fields.start_params,
-        algorithm=extra_fields.algorithm,
-        direction=extra_fields.direction.value,
-        n_free=extra_fields.n_free,
-        message=raw_res.message,
-        success=raw_res.success,
-        n_fun_evals=raw_res.n_fun_evals,
-        n_jac_evals=raw_res.n_jac_evals,
-        n_hess_evals=raw_res.n_hess_evals,
-        n_iterations=raw_res.n_iterations,
-        status=raw_res.status,
-        jac=raw_res.jac,
-        hess=raw_res.hess,
-        hess_inv=raw_res.hess_inv,
-        max_constraint_violation=raw_res.max_constraint_violation,
-        history=raw_res.history,
-        algorithm_output=raw_res.info,
-        convergence_report=conv_report,
-    )
-    return out
+from optimagic.typing import Direction, ExtraResultFields
 
 
 def process_multistart_result(
-    raw_res: InternalOptimizeResult,
+    raw_res: OptimizeResult,
     converter: Converter,
-    solver_type: AggregationLevel,
     extra_fields: ExtraResultFields,
+    multistart_info: dict[str, Any],
 ) -> OptimizeResult:
     """Process results of internal optimizers."""
-    if raw_res.multistart_info is None:
-        raise ValueError("Multistart info is missing.")
 
     if isinstance(raw_res, str):
         res = _dummy_result_from_traceback(raw_res, extra_fields)
     else:
-        res = process_single_result(
-            raw_res=raw_res,
-            converter=converter,
-            solver_type=solver_type,
-            extra_fields=extra_fields,
-        )
-
+        res = raw_res
         info = _process_multistart_info(
-            raw_res.multistart_info,
+            multistart_info,
             converter=converter,
-            solver_type=solver_type,
             extra_fields=extra_fields,
         )
 
@@ -118,24 +56,15 @@ def process_multistart_result(
 def _process_multistart_info(
     info: dict[str, Any],
     converter: Converter,
-    solver_type: AggregationLevel,
     extra_fields: ExtraResultFields,
 ) -> MultistartInfo:
     starts = [converter.params_from_internal(x) for x in info["start_parameters"]]
 
     optima = []
     for res, start in zip(info["local_optima"], starts, strict=False):
-        replacements = {
-            "start_params": start,
-            "start_fun": None,
-        }
-
-        processed = process_single_result(
-            res,
-            converter=converter,
-            solver_type=solver_type,
-            extra_fields=replace(extra_fields, **replacements),
-        )
+        processed = copy.copy(res)
+        processed.start_params = start
+        processed.start_fun = None
         optima.append(processed)
 
     sample = [converter.params_from_internal(x) for x in info["exploration_sample"]]
diff --git a/tests/optimagic/optimization/test_multistart.py b/tests/optimagic/optimization/test_multistart.py
index 06ec00236..b774c1ef7 100644
--- a/tests/optimagic/optimization/test_multistart.py
+++ b/tests/optimagic/optimization/test_multistart.py
@@ -6,13 +6,13 @@
 import pytest
 from numpy.testing import assert_array_almost_equal as aaae
 
-from optimagic.optimization.algorithm import InternalOptimizeResult
 from optimagic.optimization.multistart import (
     _draw_exploration_sample,
     get_batched_optimization_sample,
     run_explorations,
     update_convergence_state,
 )
+from optimagic.optimization.optimize_result import OptimizeResult
 
 
 @pytest.fixture()
@@ -129,13 +129,23 @@ def starts():
 
 @pytest.fixture()
 def results():
-    res = InternalOptimizeResult(
-        x=np.arange(3) + 1e-10,
+    res = OptimizeResult(
+        params=np.arange(3) + 1e-10,
         fun=4,
+        start_fun=5,
+        start_params=np.arange(3),
+        algorithm="bla",
+        direction="minimize",
+        n_free=3,
     )
     return [res]
 
 
+class DummyConverter:
+    def params_to_internal(self, params):
+        return params
+
+
 def test_update_state_converged(current_state, starts, results):
     criteria = {
         "xtol": 1e-3,
@@ -148,6 +158,7 @@ def test_update_state_converged(current_state, starts, results):
         results=results,
         convergence_criteria=criteria,
         solver_type="value",
+        converter=DummyConverter(),
     )
 
     aaae(new_state["best_x"], np.arange(3))
@@ -171,6 +182,7 @@ def test_update_state_not_converged(current_state, starts, results):
         results=results,
         convergence_criteria=criteria,
         solver_type="value",
+        converter=DummyConverter(),
     )
 
     assert not is_converged