diff --git a/baybe/constraints/continuous.py b/baybe/constraints/continuous.py
index db128e012..089c3df06 100644
--- a/baybe/constraints/continuous.py
+++ b/baybe/constraints/continuous.py
@@ -1,6 +1,8 @@
 """Continuous constraints."""
 
 import math
+from itertools import combinations
+from math import comb
 
 import numpy as np
 from attrs import define
@@ -46,6 +48,28 @@ class ContinuousCardinalityConstraint(
 ):
     """Class for continuous cardinality constraints."""
 
+    @property
+    def combinatorial_counts_zero_parameters(self) -> int:
+        """Return the total number of all possible combinations of zero parameters."""
+        combinatorial_counts = 0
+        for i_zeros in range(
+            len(self.parameters) - self.max_cardinality,
+            len(self.parameters) - self.min_cardinality + 1,
+        ):
+            combinatorial_counts += comb(len(self.parameters), i_zeros)
+        return combinatorial_counts
+
+    @property
+    def combinatorial_zero_parameters(self) -> list[tuple[str, ...]]:
+        """Return a combinatorial list of all possible zero parameters."""
+        combinatorial_zeros = []
+        for i_zeros in range(
+            len(self.parameters) - self.max_cardinality,
+            len(self.parameters) - self.min_cardinality + 1,
+        ):
+            combinatorial_zeros.extend(combinations(self.parameters, i_zeros))
+        return combinatorial_zeros
+
     def sample_inactive_parameters(self, batch_size: int = 1) -> list[set[str]]:
         """Sample sets of inactive parameters according to the cardinality constraints.
 
diff --git a/baybe/recommenders/pure/bayesian/botorch.py b/baybe/recommenders/pure/bayesian/botorch.py
index 1cec8f532..46c785bfb 100644
--- a/baybe/recommenders/pure/bayesian/botorch.py
+++ b/baybe/recommenders/pure/bayesian/botorch.py
@@ -20,7 +20,7 @@
     sample_numerical_df,
 )
 
-N_RESTART_CARDINALITY = 5
+N_ITER_THRESHOLD = 10
 
 
 @define(kw_only=True)
@@ -185,11 +185,34 @@ def _recommend_continuous_on_subspace(
         if len(subspace_continuous.constraints_cardinality):
             acqf_values_all: list[Tensor] = []
             points_all: list[Tensor] = []
-            for _ in range(N_RESTART_CARDINALITY):
-                # Randomly set some parameters inactive
-                inactive_params_sample = (
-                    subspace_continuous._sample_inactive_parameters(1)[0]
+
+            # When the size of the full list of inactive parameters is not too large,
+            # we can iterate through the full list; otherwise we randomly set some
+            # parameters inactive.
+            _iterator = (
+                subspace_continuous.combinatorial_zero_parameters
+                if (
+                    combinatorial_counts
+                    := subspace_continuous.combinatorial_counts_zero_parameters
                 )
+                <= N_ITER_THRESHOLD
+                else range(N_ITER_THRESHOLD)
+            )
+
+            for inactive_params_generator in _iterator:
+                if combinatorial_counts <= N_ITER_THRESHOLD:
+                    # Iterate through the combinations of all possible inactive
+                    # parameters.
+                    inactive_params_sample = {
+                        param
+                        for sublist in inactive_params_generator
+                        for param in sublist
+                    }
+                else:
+                    # Randomly set some parameters inactive
+                    inactive_params_sample = (
+                        subspace_continuous._sample_inactive_parameters(1)[0]
+                    )
 
                 if len(inactive_params_sample):
                     # Turn inactive parameters to fixed features (used as input in
diff --git a/baybe/searchspace/continuous.py b/baybe/searchspace/continuous.py
index 47a0ea848..494746b75 100644
--- a/baybe/searchspace/continuous.py
+++ b/baybe/searchspace/continuous.py
@@ -3,8 +3,9 @@
 from __future__ import annotations
 
 import warnings
-from collections.abc import Collection, Sequence
-from itertools import chain
+from collections.abc import Collection, Iterable, Sequence
+from functools import reduce
+from itertools import chain, product
 from typing import TYPE_CHECKING, Any, cast
 
 import numpy as np
@@ -111,6 +112,36 @@ def constraints_cardinality(self) -> tuple[ContinuousCardinalityConstraint, ...]
             if isinstance(c, ContinuousCardinalityConstraint)
         )
 
+    @property
+    def combinatorial_counts_zero_parameters(self) -> int:
+        """Return the total number of all possible combinations of zero parameters."""
+        # Note that both continuous subspace and continuous cardinality constraint
+        # have this property. This property is the counts for the subspace
+        # parameters; while the latter one is the counts only for that constraint.
+        if self.constraints_cardinality:
+            return reduce(
+                lambda x, y: x * y,
+                [
+                    con.combinatorial_counts_zero_parameters
+                    for con in self.constraints_cardinality
+                ],
+            )
+        else:
+            return 0
+
+    @property
+    def combinatorial_zero_parameters(self) -> Iterable[tuple[str, ...]]:
+        """Return a combinatorial list of all possible zero parameters on subspace."""
+        # The comments on the difference in `combinatorial_counts_zero_parameters`
+        # applies here as well.
+        if self.constraints_cardinality:
+            return product(
+                *[
+                    con.combinatorial_zero_parameters
+                    for con in self.constraints_cardinality
+                ]
+            )
+
     @constraints_nonlin.validator
     def _validate_constraints_nonlin(self, _, __) -> None:
         """Validate nonlinear constraints."""