diff --git a/pytensor/compile/debugmode.py b/pytensor/compile/debugmode.py
index 52a4e6f305..3b35cc2cd5 100644
--- a/pytensor/compile/debugmode.py
+++ b/pytensor/compile/debugmode.py
@@ -1331,7 +1331,11 @@ def printstuff(self):
 # the external requirements of the .linker attribute of a mode
 # 1) it's a class instance
 # 2) it a has a .clone() method
+# 3) it has required_rewrites and incompatible_rewrites class attributes
 class _DummyLinker:
+    required_rewrites = ()
+    incompatible_rewrites = ()
+
     # This is not a real linker anyway
     def clone(self, allow_gc=None):
         return self
diff --git a/pytensor/compile/mode.py b/pytensor/compile/mode.py
index 7d8afb9136..8cf612bff9 100644
--- a/pytensor/compile/mode.py
+++ b/pytensor/compile/mode.py
@@ -352,7 +352,14 @@ def __setstate__(self, state):
         if isinstance(optimizer, str) or optimizer is None:
             optimizer = predefined_optimizers[optimizer]
         if isinstance(optimizer, RewriteDatabaseQuery):
+            # TODO: From the __init__ signature this should always be the case
+            # But some tests and internal logic allow passing a GraphRewriter directly as optimizer
+            # Cleanup!
             self.provided_optimizer = optimizer
+            if r := linker.required_rewrites:
+                optimizer = optimizer.including(*r)
+            if r := linker.incompatible_rewrites:
+                optimizer = optimizer.excluding(*r)
         self._optimizer = optimizer
         self.call_time = 0
         self.fn_time = 0
@@ -365,14 +372,13 @@ def __str__(self):
             f"optdb={self.optdb})"
         )
 
-    def __get_optimizer(self):
+    @property
+    def optimizer(self):
         if isinstance(self._optimizer, RewriteDatabaseQuery):
             return self.optdb.query(self._optimizer)
         else:
             return self._optimizer
 
-    optimizer = property(__get_optimizer)
-
     def get_linker_optimizer(self, linker, optimizer):
         if isinstance(linker, str) or linker is None:
             linker = predefined_linkers[linker]
@@ -466,61 +472,21 @@ def clone(self, link_kwargs=None, optimizer="", **kwargs):
 
 NUMBA = Mode(
     NumbaLinker(),
-    RewriteDatabaseQuery(
-        include=["fast_run", "numba"],
-        exclude=[
-            "cxx_only",
-            "BlasOpt",
-            "local_careduce_fusion",
-            "scan_save_mem_prealloc",
-        ],
-    ),
+    RewriteDatabaseQuery(include=["fast_run", "numba"]),
 )
 
 JAX = Mode(
     JAXLinker(),
-    RewriteDatabaseQuery(
-        include=["fast_run", "jax"],
-        exclude=[
-            "cxx_only",
-            "BlasOpt",
-            "fusion",
-            "inplace",
-            "scan_save_mem_prealloc",
-            # There are specific variants for the LU decompositions supported by JAX
-            "reuse_lu_decomposition_multiple_solves",
-            "scan_split_non_sequence_lu_decomposition_solve",
-        ],
-    ),
+    RewriteDatabaseQuery(include=["fast_run", "jax"]),
 )
 PYTORCH = Mode(
     PytorchLinker(),
-    RewriteDatabaseQuery(
-        include=["fast_run"],
-        exclude=[
-            "cxx_only",
-            "BlasOpt",
-            "fusion",
-            "inplace",
-            "scan_save_mem_prealloc",
-            "reuse_lu_decomposition_multiple_solves",
-            "scan_split_non_sequence_lu_decomposition_solve",
-        ],
-    ),
+    RewriteDatabaseQuery(include=["fast_run"]),
 )
 
 MLX = Mode(
     MLXLinker(),
-    RewriteDatabaseQuery(
-        include=["fast_run"],
-        exclude=[
-            "cxx_only",
-            "BlasOpt",
-            "fusion",
-            "inplace",
-            "scan_save_mem_prealloc",
-        ],
-    ),
+    RewriteDatabaseQuery(include=["fast_run"]),
 )
 
 
diff --git a/pytensor/link/basic.py b/pytensor/link/basic.py
index 1c79d28289..f628da59b7 100644
--- a/pytensor/link/basic.py
+++ b/pytensor/link/basic.py
@@ -157,6 +157,9 @@ class Linker(ABC):
         the FunctionGraph.
     """
 
+    required_rewrites: tuple[str, ...] = ("minimum_compile",)
+    incompatible_rewrites: tuple[str, ...] = ()
+
     def __init__(
         self,
         *,
@@ -656,21 +659,37 @@ def create_jitable_thunk(
         thunk_outputs = [storage_map[n] for n in self.fgraph.outputs]
         fgraph_jit = self.jit_compile(converted_fgraph)
 
-        def thunk(
-            fgraph_jit=fgraph_jit,
-            thunk_inputs=thunk_inputs,
-            thunk_outputs=thunk_outputs,
-        ):
-            try:
-                outputs = fgraph_jit(*(x[0] for x in thunk_inputs))
-            except Exception:
-                # TODO: Should we add a fake node that combines all outputs,
-                #  since the error may come from any of them?
-                raise_with_op(self.fgraph, output_nodes[0], thunk)
+        if thunk_outputs:
 
-            # zip strict not specified because we are in a hot loop
-            for o_storage, o_val in zip(thunk_outputs, outputs):
-                o_storage[0] = o_val
+            def thunk(
+                fgraph_jit=fgraph_jit,
+                thunk_inputs=thunk_inputs,
+                thunk_outputs=thunk_outputs,
+            ):
+                try:
+                    outputs = fgraph_jit(*(x[0] for x in thunk_inputs))
+                except Exception:
+                    # TODO: Should we add a fake node that combines all outputs,
+                    #  since the error may come from any of them?
+                    raise_with_op(self.fgraph, output_nodes[0], thunk)
+
+                # zip strict not specified because we are in a hot loop
+                for o_storage, o_val in zip(thunk_outputs, outputs):
+                    o_storage[0] = o_val
+
+        else:
+            # Edge case - functions without outputs
+            def thunk(
+                fgraph_jit=fgraph_jit,
+                thunk_inputs=thunk_inputs,
+                thunk_outputs=thunk_outputs,
+            ):
+                try:
+                    res = fgraph_jit(*(x[0] for x in thunk_inputs))
+                except Exception:
+                    raise_with_op(self.fgraph, output_nodes[0], thunk)
+                assert res is None
+                return thunk_outputs
 
         thunk.inputs = thunk_inputs
         thunk.outputs = thunk_outputs
@@ -714,3 +733,7 @@ def make_all(self, input_storage=None, output_storage=None, storage_map=None):
             thunks,
             nodes,
         )
+
+    def __repr__(self):
+        # Assumes no subclass needs init arguments
+        return f"{self.__class__.__name__}()"
diff --git a/pytensor/link/jax/linker.py b/pytensor/link/jax/linker.py
index dd634e630c..6abf467824 100644
--- a/pytensor/link/jax/linker.py
+++ b/pytensor/link/jax/linker.py
@@ -9,6 +9,22 @@
 class JAXLinker(JITLinker):
     """A `Linker` that JIT-compiles NumPy-based operations using JAX."""
 
+    required_rewrites = (
+        "minimum_compile",
+        "jax",
+    )  # TODO: Distinguish between optional "jax" and "minimum_compile_jax"
+    incompatible_rewrites = (
+        "cxx",
+        "BlasOpt",
+        "local_careduce_fusion",
+        "scan_save_mem_prealloc",
+        # JAX does it his own inplace optimization
+        "inplace",
+        # There are specific variants for the LU decompositions supported by JAX
+        "reuse_lu_decomposition_multiple_solves",
+        "scan_split_non_sequence_lu_decomposition_solve",
+    )
+
     scalar_shape_inputs: tuple[int, ...]
 
     def __init__(self, *args, **kwargs):
diff --git a/pytensor/link/mlx/linker.py b/pytensor/link/mlx/linker.py
index b2f8674ea5..bccb38de7d 100644
--- a/pytensor/link/mlx/linker.py
+++ b/pytensor/link/mlx/linker.py
@@ -4,6 +4,14 @@
 class MLXLinker(JITLinker):
     """A `Linker` that JIT-compiles NumPy-based operations using Apple's MLX."""
 
+    incompatible_rewrites = (
+        "cxx_only",
+        "BlasOpt",
+        "fusion",
+        "inplace",
+        "scan_save_mem_prealloc",
+    )
+
     def __init__(self, use_compile=True, *args, **kwargs):
         super().__init__(*args, **kwargs)
         self.gen_functors = []
diff --git a/pytensor/link/numba/linker.py b/pytensor/link/numba/linker.py
index 7cc6f34454..068df4a95b 100644
--- a/pytensor/link/numba/linker.py
+++ b/pytensor/link/numba/linker.py
@@ -2,6 +2,17 @@
 
 
 class NumbaLinker(JITLinker):
+    required_rewrites = (
+        "minimum_compile",
+        "numba",
+    )  # TODO: Distinguish between optional "numba" and "minimum_compile_numba"
+    incompatible_rewrites = (
+        "cxx",
+        "BlasOpt",
+        "local_careduce_fusion",
+        "scan_save_mem_prealloc",
+    )
+
     """A `Linker` that JIT-compiles NumPy-based operations using Numba."""
 
     def fgraph_convert(self, fgraph, **kwargs):
diff --git a/pytensor/link/pytorch/linker.py b/pytensor/link/pytorch/linker.py
index 18824a5b71..8c62e3577f 100644
--- a/pytensor/link/pytorch/linker.py
+++ b/pytensor/link/pytorch/linker.py
@@ -5,6 +5,16 @@
 class PytorchLinker(JITLinker):
     """A `Linker` that compiles NumPy-based operations using torch.compile."""
 
+    incompatible_rewrites = (
+        "cxx_only",
+        "BlasOpt",
+        "fusion",
+        "inplace",
+        "scan_save_mem_prealloc",
+        "reuse_lu_decomposition_multiple_solves",
+        "scan_split_non_sequence_lu_decomposition_solve",
+    )
+
     def __init__(self, *args, **kwargs):
         super().__init__(*args, **kwargs)
         self.gen_functors = []
diff --git a/tests/compile/test_mode.py b/tests/compile/test_mode.py
index 291eac0782..48c2a6c4a0 100644
--- a/tests/compile/test_mode.py
+++ b/tests/compile/test_mode.py
@@ -55,11 +55,15 @@ def test_NoOutputFromInplace():
 
 
 def test_including():
-    mode = Mode(optimizer="merge")
-    assert set(mode._optimizer.include) == {"merge"}
+    mode = Mode(linker="py", optimizer="merge")
+    assert set(mode._optimizer.include) == {"minimum_compile", "merge"}
 
     new_mode = mode.including("fast_compile")
-    assert set(new_mode._optimizer.include) == {"merge", "fast_compile"}
+    assert set(new_mode._optimizer.include) == {
+        "minimum_compile",
+        "merge",
+        "fast_compile",
+    }
 
 
 class TestBunchOfModes: