diff --git a/nevergrad/ops/__init__.py b/nevergrad/ops/__init__.py
new file mode 100644
index 000000000..f0271cc44
--- /dev/null
+++ b/nevergrad/ops/__init__.py
@@ -0,0 +1,4 @@
+# Copyright (c) Facebook, Inc. and its affiliates. All Rights Reserved.
+#
+# This source code is licensed under the MIT license found in the
+# LICENSE file in the root directory of this source tree.
diff --git a/nevergrad/ops/constraints.py b/nevergrad/ops/constraints.py
new file mode 100644
index 000000000..0256a698c
--- /dev/null
+++ b/nevergrad/ops/constraints.py
@@ -0,0 +1,94 @@
+# Copyright (c) Facebook, Inc. and its affiliates. All Rights Reserved.
+#
+# This source code is licensed under the MIT license found in the
+# LICENSE file in the root directory of this source tree.
+
+import numpy as np
+import nevergrad.common.typing as tp
+from nevergrad.common import errors
+from nevergrad.parametrization import core
+from nevergrad import optimizers
+from nevergrad import callbacks
+
+
+class Constraint(core.Operator):
+    """Operator for applying a constraint on a Parameter
+
+    Parameters
+    ----------
+    func: function
+        the constraint function, taking the same arguments that the function to optimize.
+        This constraint function must return a float (or a list/tuple/array of floats),
+        positive if the constraint is not satisfied, null or negative otherwise.
+    optimizer: str
+        name of the optimizer to use for solving the constraint
+    budget: int
+        the budget to use for applying the constraint
+
+    Example
+    -------
+    >>> constrained_parameter = Constraint(constraint_function)(parameter)
+    >>> constrained_parameter.value  # value after trying to satisfy the constraint
+    """
+
+    _LAYER_LEVEL = core.Level.CONSTRAINT
+
+    def __init__(self, func: tp.Callable[..., tp.Loss], optimizer: str = "NGOpt", budget: int = 100) -> None:
+        super().__init__()
+        self._func = func
+        self._opt_cls = optimizers.registry[optimizer]
+        self._budget = budget
+        self._cache: tp.Any = None
+
+    def _layered_del_value(self) -> None:
+        self._cache = None  # clear cache!
+
+    def apply_constraint(self, parameter: core.Parameter) -> core.Parameter:
+        """Find a new parameter that better satisfies the constraint"""
+        # This function can be overriden
+        optim = self._opt_cls(parameter, budget=self._budget)
+        early_stopping = callbacks.EarlyStopping(self.stopping_criterion)
+        optim.register_callback("ask", early_stopping)
+        optim.minimize(self.function)
+        return optim.pareto_front()[0]
+
+    def function(self, *args: tp.Any, **kwargs: tp.Any) -> tp.Loss:
+        out = self._func(*args, **kwargs)
+        if isinstance(out, (bool, np.bool)):
+            raise errors.NevergradTypeError(
+                "Constraint must be a positive float if unsatisfied constraint (not bool)"
+            )
+        return np.maximum(0, out)  # type: ignore
+
+    def parameter(self) -> core.Parameter:
+        """Returns a constraint-free parameter, for the optimization process"""
+        param = self._layers[0].copy()
+        # remove last layer and make sure it is the last one
+        if self._index != param._layers.pop()._index:
+            raise RuntimeError("Constraint layer should be unique and placed last")
+        return param  # type: ignore
+
+    def stopping_criterion(self, optimizer: tp.Any) -> bool:
+        """Checks whether a solution was found
+        This is used as stopping criterio callback
+        """
+        if optimizer.num_tell < 1:
+            return False
+        best = optimizer.pareto_front()[0]
+        return not np.any(best.losses > 0)
+
+    def _layered_get_value(self) -> tp.Any:
+        # TODO: this can be made more efficient (fewer copy) if need be.
+        # Override only apply_constraint if you can, tampering with this method is tricky
+        if self._cache is not None:
+            return self._cache
+        parameter = self.parameter()
+        satisfied = not np.any(self.function(*parameter.args, **parameter.kwargs))
+        if satisfied:
+            self._cache = parameter.value
+            return self._cache
+        root: core.Parameter = self._layers[0]  # type: ignore
+        recom = self.apply_constraint(parameter)
+        root.set_standardized_data(np.zeros(root.dimension), reference=recom)
+        self._cache = recom.value
+        return self._cache
diff --git a/nevergrad/ops/test_constraints.py b/nevergrad/ops/test_constraints.py
new file mode 100644
index 000000000..b873c333c
--- /dev/null
+++ b/nevergrad/ops/test_constraints.py
@@ -0,0 +1,27 @@
+# Copyright (c) Facebook, Inc. and its affiliates. All Rights Reserved.
+#
+# This source code is licensed under the MIT license found in the
+# LICENSE file in the root directory of this source tree.
+
+import typing as tp
+import pytest
+import numpy as np
+import nevergrad as ng
+from . import constraints
+
+
+def function(*args: float) -> tp.Any:
+    if len(args) == 1:
+        return args[0]
+    return args
+
+
+@pytest.mark.parametrize("num", (1, 3))  # type: ignore
+def test_constraint(num: int) -> None:
+    parameter = ng.p.Instrumentation(*(ng.p.Scalar(np.random.randn()) for _ in range(num)))
+    constrained = constraints.Constraint(function)(parameter)
+    # check basic layer functionalities
+    layer: constraints.Constraint = constrained._layers[-1]  # type: ignore
+    assert layer.function(*([1] * num)) == 1 if num == 1 else [1] * num
+    assert layer.function(*([-1] * num)) == 0 if num == 1 else [0] * num
+    assert sum(x < 0.1 for x in constrained.args) == num, constrained.args  # some slack to avoid flakiness
diff --git a/nevergrad/optimization/base.py b/nevergrad/optimization/base.py
index 5bc07ba57..b46f2762f 100644
--- a/nevergrad/optimization/base.py
+++ b/nevergrad/optimization/base.py
@@ -467,6 +467,8 @@ def ask(self) -> p.Parameter:
         assert (
             candidate is not None
         ), f"{self.__class__.__name__}._internal_ask method returned None instead of a point."
+        # make sure to call value getter which may update the value, before we freeze the paremeter
+        candidate.value  # pylint: disable=pointless-statement
         candidate.freeze()  # make sure it is not modified somewhere
         return candidate
 
diff --git a/nevergrad/optimization/test_optimizerlib.py b/nevergrad/optimization/test_optimizerlib.py
index 647837bd0..83119f0af 100644
--- a/nevergrad/optimization/test_optimizerlib.py
+++ b/nevergrad/optimization/test_optimizerlib.py
@@ -518,17 +518,19 @@ def _ellips(x: np.ndarray) -> float:
         assert _target(default_recom) > 7.0 * _target(metamodel_recom)
 
 
-@pytest.mark.parametrize(
-    "penalization,expected",
+@pytest.mark.parametrize(  # type: ignore
+    "penalization,expected,as_layer",
     [
-        (False, [1.005573e00, 3.965783e-04]),
-        (True, [0.999987, -0.322118]),
+        (False, [1.005573e00, 3.965783e-04], False),
+        (True, [0.999987, -0.322118], False),
+        (False, [1.000760, -5.116619e-4], True),
     ],
 )
 @testing.suppress_nevergrad_warnings()  # hides failed constraints
-def test_constrained_optimization(penalization: bool, expected: tp.List[float]) -> None:
+def test_constrained_optimization(penalization: bool, expected: tp.List[float], as_layer: bool) -> None:
     def constraint(i: tp.Any) -> tp.Union[bool, float]:
-        return i[1]["x"][0] >= 1
+        out = i[1]["x"][0] >= 1
+        return out if not as_layer else float(not out)
 
     parametrization = ng.p.Instrumentation(x=ng.p.Array(shape=(1,)), y=ng.p.Scalar())
     optimizer = optlib.OnePlusOne(parametrization, budget=100)
@@ -541,8 +543,8 @@ def constraint(i: tp.Any) -> tp.Union[bool, float]:  # pylint: disable=function-
 
     with warnings.catch_warnings():
         warnings.filterwarnings("ignore", category=UserWarning)
-        optimizer.parametrization.register_cheap_constraint(constraint)
-    recom = optimizer.minimize(_square)
+        optimizer.parametrization.register_cheap_constraint(constraint, as_layer=as_layer)
+    recom = optimizer.minimize(_square, verbosity=2)
     np.testing.assert_array_almost_equal([recom.kwargs["x"][0], recom.kwargs["y"]], expected)
 
 
diff --git a/nevergrad/parametrization/_layering.py b/nevergrad/parametrization/_layering.py
index 127d82b09..9aa7c53b4 100644
--- a/nevergrad/parametrization/_layering.py
+++ b/nevergrad/parametrization/_layering.py
@@ -22,8 +22,9 @@ class Level(Enum):
     OPERATION = 10
 
     # final
-    ARRAY_CASTING = 900
-    INTEGER_CASTING = 1000  # must be the last layer
+    ARRAY_CASTING = 800
+    INTEGER_CASTING = 900
+    CONSTRAINT = 1000  # must be the last layer
 
 
 class Layered:
diff --git a/nevergrad/parametrization/container.py b/nevergrad/parametrization/container.py
index dfe5fbfc9..80c356dc9 100644
--- a/nevergrad/parametrization/container.py
+++ b/nevergrad/parametrization/container.py
@@ -42,6 +42,10 @@ def __init__(self, **parameters: tp.Any) -> None:
             str, str
         ] = {}  # hacky undocumented way to bypass boring representations
 
+    @property
+    def dimension(self) -> int:
+        return sum(x.dimension for x in self._content.values())
+
     def _sanity_check(self, parameters: tp.List[core.Parameter]) -> None:
         """Check that all parameters are different"""
         # TODO: this is first order, in practice we would need to test all the different
@@ -230,10 +234,10 @@ def __init__(self, *args: tp.Any, **kwargs: tp.Any) -> None:
 
     @property
     def args(self) -> tp.Tuple[tp.Any, ...]:
-        return self[0].value  # type: ignore
+        return self.value[0]  # type: ignore
 
     @property
     def kwargs(self) -> tp.Dict[str, tp.Any]:
-        return self[1].value  # type: ignore
+        return self.value[1]  # type: ignore
 
     value: core.ValueProperty[tp.ArgsKwargs] = core.ValueProperty()  # type: ignore
diff --git a/nevergrad/parametrization/core.py b/nevergrad/parametrization/core.py
index 95b10f451..9dcd82bfc 100644
--- a/nevergrad/parametrization/core.py
+++ b/nevergrad/parametrization/core.py
@@ -11,10 +11,10 @@
 from . import utils
 from ._layering import ValueProperty as ValueProperty
 from ._layering import Layered as Layered
-from ._layering import Level
+from ._layering import Level as Level
 
 
-# pylint: disable=no-value-for-parameter,pointless-statement
+# pylint: disable=no-value-for-parameter,pointless-statement,import-outside-toplevel
 
 
 P = tp.TypeVar("P", bound="Parameter")
@@ -266,7 +266,9 @@ def satisfies_constraints(self) -> bool:
         return all(utils.float_penalty(func(val)) <= 0 for func in self._constraint_checkers)
 
     def register_cheap_constraint(
-        self, func: tp.Union[tp.Callable[[tp.Any], bool], tp.Callable[[tp.Any], float]]
+        self,
+        func: tp.Union[tp.Callable[[tp.Any], bool], tp.Callable[[tp.Any], float]],
+        as_layer: bool = False,
     ) -> None:
         """Registers a new constraint on the parameter values.
 
@@ -281,10 +283,23 @@ def register_cheap_constraint(
         - this is only for checking after mutation/recombination/etc if the value still satisfy the constraints.
           The constraint is not used in those processes.
         - constraints should be fast to compute.
+        - this function has an additional "as_layer" parameter which is experimental for now, and can have unexpected
+          behavior
         """
         if getattr(func, "__name__", "not lambda") == "<lambda>":  # LambdaType does not work :(
             warnings.warn("Lambda as constraint is not advised because it may not be picklable.")
-        self._constraint_checkers.append(func)
+        if not as_layer:
+            self._constraint_checkers.append(func)
+        else:
+            from nevergrad.ops.constraints import Constraint
+            import nevergrad as ng
+
+            compat_func = (
+                func
+                if not isinstance(self, ng.p.Instrumentation)
+                else utils._ConstraintCompatibilityFunction(func)
+            )
+            self.add_layer(Constraint(compat_func))  # type: ignore
 
     # %% random state
 
@@ -381,7 +396,7 @@ def _check_frozen(self) -> None:
             self, Constant
         ):  # nevermind constants (since they dont spawn children)
             raise RuntimeError(
-                f"Cannot modify frozen Parameter {self}, please spawn a child and modify it instead"
+                f"Cannot modify frozen Parameter {self.name}, please spawn a child and modify it instead"
                 "(optimizers freeze the parametrization and all asked and told candidates to avoid border effects)"
             )
         self._subobjects.apply("_check_frozen")
@@ -480,3 +495,15 @@ def __init__(self, parameter: tp.Optional[Parameter] = None) -> None:
                 f"be used by the optimizer.\n(received {parameter} of type {type(parameter)})"
             )
         super().__init__(parameter)
+
+
+class Operator(Layered):
+    """Layer object that can be used as an operator on a Parameter"""
+
+    _LAYER_LEVEL = Level.OPERATION
+
+    def __call__(self, parameter: Parameter) -> Parameter:
+        """Applies the operator on a Parameter to create a new Parameter"""
+        new = parameter.copy()
+        new.add_layer(self.copy())
+        return new
diff --git a/nevergrad/parametrization/data.py b/nevergrad/parametrization/data.py
index 30dc0c624..443c82b77 100644
--- a/nevergrad/parametrization/data.py
+++ b/nevergrad/parametrization/data.py
@@ -127,6 +127,10 @@ def __init__(
         self._ref_data: tp.Optional[np.ndarray] = None
         self.add_layer(_layering.ArrayCasting())
 
+    @property
+    def dimension(self) -> int:
+        return int(np.prod(self._value.shape))
+
     def _compute_descriptors(self) -> utils.Descriptors:
         return utils.Descriptors(continuous=not self.integer)
 
diff --git a/nevergrad/parametrization/utils.py b/nevergrad/parametrization/utils.py
index 5568f4a9f..f9549df29 100644
--- a/nevergrad/parametrization/utils.py
+++ b/nevergrad/parametrization/utils.py
@@ -294,3 +294,15 @@ def float_penalty(x: tp.Union[bool, float]) -> float:
     elif isinstance(x, (float, np.float)):
         return -min(0, x)  # Negative ==> >0
     raise TypeError(f"Only bools and floats are supported for check constaint, but got: {x} ({type(x)})")
+
+
+class _ConstraintCompatibilityFunction:
+    """temporary hack for "register_cheap_constraint", to be removed"""
+
+    def __init__(self, func: tp.Callable[[tp.Any], tp.Loss]) -> None:
+        self.func = func
+
+    def __call__(self, *args: tp.Any, **kwargs: tp.Any) -> tp.Loss:
+        out = self.func((args, kwargs))
+        print("calling", args, kwargs, "out =", out)
+        return out