diff --git a/conftest.py b/conftest.py
index 32ba7bae0..1558dd054 100644
--- a/conftest.py
+++ b/conftest.py
@@ -9,7 +9,6 @@
 import pytest
 import torch
 from concrete.fhe import Graph as CPGraph
-from concrete.fhe import ParameterSelectionStrategy
 from concrete.fhe.compilation import Circuit, Configuration
 from concrete.fhe.mlir.utils import MAXIMUM_TLU_BIT_WIDTH
 from sklearn.datasets import make_classification, make_regression
@@ -147,9 +146,6 @@ def pytest_sessionfinish(session: pytest.Session, exitstatus):  # pylint: disabl
 def default_configuration():
     """Return the default test compilation configuration."""
 
-    # Remove parameter_selection_strategy once it is set to multi-parameter in Concrete Python
-    # by default
-    # FIXME: https://github.com/zama-ai/concrete-ml-internal/issues/3860
     # Parameter `enable_unsafe_features` and `use_insecure_key_cache` are needed in order to be
     # able to cache generated keys through `insecure_key_cache_location`. As the name suggests,
     # these parameters are unsafe and should only be used for debugging in development
@@ -158,7 +154,6 @@ def default_configuration():
         enable_unsafe_features=True,
         use_insecure_key_cache=True,
         insecure_key_cache_location="ConcreteNumpyKeyCache",
-        parameter_selection_strategy=ParameterSelectionStrategy.MULTI,
     )
 
 
diff --git a/src/concrete/ml/common/utils.py b/src/concrete/ml/common/utils.py
index 4414056fb..5e08cbe71 100644
--- a/src/concrete/ml/common/utils.py
+++ b/src/concrete/ml/common/utils.py
@@ -2,7 +2,6 @@
 
 import enum
 import string
-import warnings
 from functools import partial
 from types import FunctionType
 from typing import Any, Callable, Dict, Iterable, List, Optional, Tuple, Union
@@ -587,43 +586,9 @@ def all_values_are_of_dtype(*values: Any, dtypes: Union[str, List[str]]) -> bool
     return all(_is_of_dtype(value, supported_dtypes) for value in values)
 
 
-def set_multi_parameter_in_configuration(configuration: Optional[Configuration], **kwargs):
-    """Build a Configuration instance with multi-parameter strategy, unless one is already given.
-
-    If the given Configuration instance is not None and the parameter strategy is set to MONO, a
-    warning is raised in order to make sure the user did it on purpose.
-
-    Args:
-        configuration (Optional[Configuration]): The configuration to consider.
-        **kwargs: Additional parameters to use for instantiating a new Configuration instance, if
-            configuration is None.
-
-    Returns:
-        configuration (Configuration): A configuration with multi-parameter strategy.
-    """
-    assert (
-        "parameter_selection_strategy" not in kwargs
-    ), "Please do not provide a parameter_selection_strategy parameter as it will be set to MULTI."
-    if configuration is None:
-        configuration = Configuration(
-            parameter_selection_strategy=ParameterSelectionStrategy.MULTI, **kwargs
-        )
-
-    elif configuration.parameter_selection_strategy == ParameterSelectionStrategy.MONO:
-        warnings.warn(
-            "Setting the parameter_selection_strategy to mono-parameter is not recommended as it "
-            "can deteriorate performances. If you set it voluntarily, this message can be ignored. "
-            "Else, please set parameter_selection_strategy to ParameterSelectionStrategy.MULTI "
-            "when initializing the Configuration instance.",
-            stacklevel=2,
-        )
-
-    return configuration
-
-
-# Remove this function once Concrete Python fixes the multi-parameter bug with fully-leveled
+# Remove this function once Concrete Python fixes the multi-parameter bug with KNN
 # circuits
-# TODO: https://github.com/zama-ai/concrete-ml-internal/issues/3862
+# FIXME: https://github.com/zama-ai/concrete-ml-internal/issues/3978
 def force_mono_parameter_in_configuration(configuration: Optional[Configuration], **kwargs):
     """Force configuration to mono-parameter strategy.
 
diff --git a/src/concrete/ml/quantization/quantized_module.py b/src/concrete/ml/quantization/quantized_module.py
index d0456a6bd..0fb81e4de 100644
--- a/src/concrete/ml/quantization/quantized_module.py
+++ b/src/concrete/ml/quantization/quantized_module.py
@@ -24,7 +24,6 @@
     check_there_is_no_p_error_options_in_configuration,
     generate_proxy_function,
     manage_parameters_for_pbs_errors,
-    set_multi_parameter_in_configuration,
     to_tuple,
 )
 from .base_quantized_op import ONNXOpInputOutputType, QuantizedOp
@@ -639,11 +638,6 @@ def compile(
         # Find the right way to set parameters for compiler, depending on the way we want to default
         p_error, global_p_error = manage_parameters_for_pbs_errors(p_error, global_p_error)
 
-        # Remove this function once the default strategy is set to multi-parameter in Concrete
-        # Python
-        # TODO: https://github.com/zama-ai/concrete-ml-internal/issues/3860
-        configuration = set_multi_parameter_in_configuration(configuration)
-
         # Jit compiler is now deprecated and will soon be removed, it is thus forced to False
         # by default
         self.fhe_circuit = compiler.compile(
diff --git a/src/concrete/ml/sklearn/base.py b/src/concrete/ml/sklearn/base.py
index 052343d84..eaf228def 100644
--- a/src/concrete/ml/sklearn/base.py
+++ b/src/concrete/ml/sklearn/base.py
@@ -38,7 +38,6 @@
     force_mono_parameter_in_configuration,
     generate_proxy_function,
     manage_parameters_for_pbs_errors,
-    set_multi_parameter_in_configuration,
 )
 from ..onnx.convert import OPSET_VERSION_FOR_ONNX_EXPORT
 from ..onnx.onnx_model_manipulations import clean_graph_after_node_op_type, remove_node_types
@@ -1363,27 +1362,6 @@ def _get_module_to_compile(self) -> Union[Compiler, QuantizedModule]:
         return compiler
 
     def compile(self, *args, **kwargs) -> Circuit:
-
-        # Factorize this in the base class once Concrete Python fixes the multi-parameter bug
-        # with fully-leveled circuits
-        # TODO: https://github.com/zama-ai/concrete-ml-internal/issues/3862
-        # Remove this function once the default strategy is set to multi-parameter in Concrete
-        # Python
-        # TODO: https://github.com/zama-ai/concrete-ml-internal/issues/3860
-        # If a configuration instance is given as a positional parameter, set the strategy to
-        # multi-parameter
-        if len(args) >= 2:
-            configuration = set_multi_parameter_in_configuration(args[1])
-            args_list = list(args)
-            args_list[1] = configuration
-            args = tuple(args_list)
-
-        # Else, retrieve the configuration in kwargs if it exists, or create a new one, and set the
-        # strategy to multi-parameter
-        else:
-            configuration = kwargs.get("configuration", None)
-            kwargs["configuration"] = set_multi_parameter_in_configuration(configuration)
-
         BaseEstimator.compile(self, *args, **kwargs)
 
         # Check that the graph only has a single output
@@ -1638,26 +1616,6 @@ def _inference(self, q_X: numpy.ndarray) -> numpy.ndarray:
         y_pred += self._q_bias
         return y_pred
 
-    # Remove this function once Concrete Python fixes the multi-parameter bug with fully-leveled
-    # circuits and factorize it in the base class
-    # TODO: https://github.com/zama-ai/concrete-ml-internal/issues/3862
-    def compile(self, *args, **kwargs) -> Circuit:
-        # If a configuration instance is given as a positional parameter, set the strategy to
-        # multi-parameter
-        if len(args) >= 2:
-            configuration = force_mono_parameter_in_configuration(args[1])
-            args_list = list(args)
-            args_list[1] = configuration
-            args = tuple(args_list)
-
-        # Else, retrieve the configuration in kwargs if it exists, or create a new one, and set the
-        # strategy to multi-parameter
-        else:
-            configuration = kwargs.get("configuration", None)
-            kwargs["configuration"] = force_mono_parameter_in_configuration(configuration)
-
-        return BaseEstimator.compile(self, *args, **kwargs)
-
 
 class SklearnLinearRegressorMixin(SklearnLinearModelMixin, sklearn.base.RegressorMixin, ABC):
     """A Mixin class for sklearn linear regressors with FHE.
diff --git a/tests/sklearn/test_sklearn_models.py b/tests/sklearn/test_sklearn_models.py
index 307e412d3..065eeb214 100644
--- a/tests/sklearn/test_sklearn_models.py
+++ b/tests/sklearn/test_sklearn_models.py
@@ -39,7 +39,6 @@
 import pandas
 import pytest
 import torch
-from concrete.fhe import ParameterSelectionStrategy
 from sklearn.decomposition import PCA
 from sklearn.exceptions import ConvergenceWarning, UndefinedMetricWarning
 from sklearn.metrics import make_scorer, matthews_corrcoef, top_k_accuracy_score
@@ -1056,19 +1055,6 @@ def check_exposition_structural_methods_decision_trees(model, x, y):
     )
 
 
-def check_mono_parameter_warnings(model, x, default_configuration):
-    """Check that setting voluntarily a mono-parameter strategy properly raises a warning."""
-
-    # Set the parameter strategy to mono-parameter
-    default_configuration.parameter_selection_strategy = ParameterSelectionStrategy.MONO
-
-    with pytest.warns(
-        UserWarning,
-        match="Setting the parameter_selection_strategy to mono-parameter is not recommended.*",
-    ):
-        model.compile(x, default_configuration)
-
-
 @pytest.mark.parametrize("model_class, parameters", sklearn_models_and_datasets)
 @pytest.mark.parametrize(
     "n_bits",
@@ -1668,35 +1654,3 @@ def test_exposition_structural_methods_decision_trees(
         print("Run check_exposition_structural_methods_decision_trees")
 
     check_exposition_structural_methods_decision_trees(model, x, y)
-
-
-@pytest.mark.parametrize("model_class, parameters", sklearn_models_and_datasets)
-def test_mono_parameter_warnings(
-    model_class,
-    parameters,
-    load_data,
-    is_weekly_option,
-    default_configuration,
-    verbose=True,
-):
-    """Test that setting voluntarily a mono-parameter strategy properly raises a warning."""
-
-    # Remove this once Concrete Python fixes the multi-parameter bug with fully-leveled circuits
-    # TODO: https://github.com/zama-ai/concrete-ml-internal/issues/3862
-    # Linear models are manually forced to use mono-parameter
-    if is_model_class_in_a_list(model_class, get_sklearn_linear_models()):
-        return
-
-    # KNN is manually forced to use mono-parameter
-    # FIXME: https://github.com/zama-ai/concrete-ml-internal/issues/3978
-    if is_model_class_in_a_list(model_class, get_sklearn_neighbors_models()):
-        return
-
-    n_bits = min(N_BITS_REGULAR_BUILDS)
-
-    model, x = preamble(model_class, parameters, n_bits, load_data, is_weekly_option)
-
-    if verbose:
-        print("Run check_mono_parameter_warnings")
-
-    check_mono_parameter_warnings(model, x, default_configuration)
diff --git a/tests/torch/test_hybrid_converter.py b/tests/torch/test_hybrid_converter.py
index 99b784e23..429fce176 100644
--- a/tests/torch/test_hybrid_converter.py
+++ b/tests/torch/test_hybrid_converter.py
@@ -6,7 +6,7 @@
 
 import pytest
 import torch
-from concrete.fhe import Configuration, ParameterSelectionStrategy
+from concrete.fhe import Configuration
 from transformers import GPT2LMHeadModel, GPT2Tokenizer
 
 from concrete.ml.torch.hybrid_model import HybridFHEModel
@@ -20,7 +20,6 @@ def run_hybrid_model_test(
     # Multi-parameter strategy is used in order to speed-up the FHE executions
     configuration = Configuration(
         single_precision=False,
-        parameter_selection_strategy=ParameterSelectionStrategy.MULTI,
     )
 
     # Create a hybrid model
diff --git a/use_case_examples/cifar/cifar_brevitas_training/evaluate_one_example_fhe.py b/use_case_examples/cifar/cifar_brevitas_training/evaluate_one_example_fhe.py
index b90fc15c7..245111516 100644
--- a/use_case_examples/cifar/cifar_brevitas_training/evaluate_one_example_fhe.py
+++ b/use_case_examples/cifar/cifar_brevitas_training/evaluate_one_example_fhe.py
@@ -80,7 +80,6 @@ def wrapper(*args, **kwargs):
     enable_unsafe_features=True,
     use_insecure_key_cache=True,
     insecure_key_cache_location=KEYGEN_CACHE_DIR,
-    parameter_selection_strategy=fhe.ParameterSelectionStrategy.MULTI,
 )
 
 print("Compiling the model.")
diff --git a/use_case_examples/cifar/cifar_brevitas_training/evaluate_torch_cml.py b/use_case_examples/cifar/cifar_brevitas_training/evaluate_torch_cml.py
index 95d6136d2..059771e66 100644
--- a/use_case_examples/cifar/cifar_brevitas_training/evaluate_torch_cml.py
+++ b/use_case_examples/cifar/cifar_brevitas_training/evaluate_torch_cml.py
@@ -3,7 +3,7 @@
 
 import numpy as np
 import torch
-from concrete.fhe import Configuration, ParameterSelectionStrategy
+from concrete.fhe import Configuration
 from models import cnv_2w2a
 from torch.utils.data import DataLoader
 from tqdm import tqdm
@@ -106,7 +106,6 @@ def main(args):
     cfg = Configuration(
         verbose=True,
         show_optimizer=args.show_optimizer,
-        parameter_selection_strategy=ParameterSelectionStrategy.MULTI,
     )
 
     for rounding_threshold_bits in rounding_threshold_bits_list:
diff --git a/use_case_examples/cifar/cifar_brevitas_with_model_splitting/infer_fhe.py b/use_case_examples/cifar/cifar_brevitas_with_model_splitting/infer_fhe.py
index 7d872f0ae..d2c14e717 100644
--- a/use_case_examples/cifar/cifar_brevitas_with_model_splitting/infer_fhe.py
+++ b/use_case_examples/cifar/cifar_brevitas_with_model_splitting/infer_fhe.py
@@ -8,7 +8,7 @@
 import torch
 import torchvision
 import torchvision.transforms as transforms
-from concrete.fhe import Circuit, Configuration, ParameterSelectionStrategy
+from concrete.fhe import Circuit, Configuration
 from model import CNV
 
 from concrete.ml.deployment.fhe_client_server import FHEModelDev
@@ -54,10 +54,7 @@ def main():
         train_features_sub_set = model.clear_module(train_sub_set)
 
     # Multi-parameter strategy is used in order to speed-up the FHE executions
-    configuration = Configuration(
-        show_optimizer=True,
-        parameter_selection_strategy=ParameterSelectionStrategy.MULTI,
-    )
+    configuration = Configuration(show_optimizer=True)
 
     compilation_onnx_path = "compilation_model.onnx"
     print("Compiling the model ...")
diff --git a/use_case_examples/cifar/cifar_brevitas_with_model_splitting/infer_fhe_simulation.py b/use_case_examples/cifar/cifar_brevitas_with_model_splitting/infer_fhe_simulation.py
index 3cc8c62ec..b537b9837 100644
--- a/use_case_examples/cifar/cifar_brevitas_with_model_splitting/infer_fhe_simulation.py
+++ b/use_case_examples/cifar/cifar_brevitas_with_model_splitting/infer_fhe_simulation.py
@@ -8,7 +8,6 @@
 import torch
 import torchvision
 from brevitas import config
-from concrete.fhe import Configuration, ParameterSelectionStrategy
 from model import CNV
 from scipy.special import softmax
 from torch.backends import cudnn
@@ -110,14 +109,6 @@ def main():
     with torch.no_grad():
         train_features_sub_set = net.clear_module(train_sub_set)
 
-    optional_kwargs = {}
-
-    # Multi-parameter strategy is used in order to speed-up the FHE executions
-    optional_kwargs["configuration"] = Configuration(
-        dump_artifacts_on_unexpected_failures=True,
-        parameter_selection_strategy=ParameterSelectionStrategy.MULTI,
-    )
-
     compilation_onnx_path = "compilation_model.onnx"
     print("Compiling the model")
     start_compile = time.time()
@@ -126,7 +117,6 @@ def main():
     quantized_numpy_module = compile_brevitas_qat_model(
         torch_model=net.encrypted_module,
         torch_inputset=train_features_sub_set,
-        **optional_kwargs,
         output_onnx_file=compilation_onnx_path,
     )
 
diff --git a/use_case_examples/mnist/MnistInFHE.ipynb b/use_case_examples/mnist/MnistInFHE.ipynb
index df3820acf..d1406beaf 100644
--- a/use_case_examples/mnist/MnistInFHE.ipynb
+++ b/use_case_examples/mnist/MnistInFHE.ipynb
@@ -22,7 +22,7 @@
     "import torch\n",
     "\n",
     "# Concrete-Python\n",
-    "from concrete.fhe import Configuration, ParameterSelectionStrategy\n",
+    "from concrete.fhe import Configuration\n",
     "\n",
     "# The QAT model\n",
     "from model import MNISTQATModel  # pylint: disable=no-name-in-module\n",
@@ -168,7 +168,6 @@
     "        enable_unsafe_features=True,\n",
     "        use_insecure_key_cache=True,\n",
     "        insecure_key_cache_location=\"/tmp/keycache\",\n",
-    "        parameter_selection_strategy=ParameterSelectionStrategy.MULTI,\n",
     "    )\n",
     "\n",
     "    if use_simulation:\n",