diff --git a/obsidian/parameters/discrete.py b/obsidian/parameters/discrete.py
index cf4730f..8a6e9b9 100644
--- a/obsidian/parameters/discrete.py
+++ b/obsidian/parameters/discrete.py
@@ -214,21 +214,29 @@ def range(self):
 
     def __init__(self,
                  name,
-                 categories: list[int | float]):
+                 categories: list[int | float],
+                 search_categories: list[int | float] = None):
         
         if not isinstance(categories, list):
             raise TypeError('Categories must be a number or list of numbers')
-               
-        self.categories = categories
-        for c in self.categories:
-            self._validate_value(c)
-        
+
         self.name = name
         self.categories = categories if isinstance(categories, list) else [categories]
         self.categories.sort()
-        for c in categories:
+        for c in self.categories:
             self._validate_value(c)
-
+        
+        # Set the search space to the parameter space by default
+        if not search_categories:
+            search_categories = self.categories
+        else:
+            if not isinstance(search_categories, list):
+                search_categories = [search_categories]
+            for c in search_categories:
+                self._validate_value(c)
+        search_categories.sort()
+        self.set_search(search_categories)
+    
     def _validate_value(self,
                         value: int | float):
         """
diff --git a/obsidian/parameters/param_space.py b/obsidian/parameters/param_space.py
index e68070b..a8e86f0 100644
--- a/obsidian/parameters/param_space.py
+++ b/obsidian/parameters/param_space.py
@@ -242,13 +242,13 @@ def search_space(self) -> pd.DataFrame:
                 X_search_t = pd.concat([X_search_t, cont_bounds], axis=1)
                 
             # For discrete, encode the available categories, then log the min-max of encoded columns
-            elif isinstance(param, Param_Discrete) and (not isinstance(param, Param_Ordinal)):
+            elif isinstance(param, Param_Discrete) and (not isinstance(param, (Param_Ordinal, Param_Discrete_Numeric))):
                 # Discrete parameter bounds aren't actually handled here; they are handled in optimizer._fixed_features())
                 cat_e = param.encode(param.search_categories)
                 disc_bounds = pd.DataFrame(np.vstack([[0]*cat_e.shape[-1], cat_e.max().values]),
                                            columns=cat_e.columns)
                 X_search_t = pd.concat([X_search_t, disc_bounds], axis=1)
-            elif isinstance(param, Param_Ordinal):
+            elif isinstance(param, (Param_Ordinal, Param_Discrete_Numeric)):
                 cat_e = param.encode(param.search_categories)
                 cont_bounds = pd.DataFrame([min(cat_e), max(cat_e)], columns=[param.name])
                 X_search_t = pd.concat([X_search_t, cont_bounds], axis=1)