diff --git a/.ci_support/migrations/cutensor2.yaml b/.ci_support/migrations/cutensor2.yaml
index 8062bd25..3bcb5800 100644
--- a/.ci_support/migrations/cutensor2.yaml
+++ b/.ci_support/migrations/cutensor2.yaml
@@ -3,7 +3,14 @@ __migrator:
   kind: version
   migration_number: 1
   bump_number: 1
-  use_local: True
+  commit_message: |
+    Rebuild for cuTENSOR 2.x support
+    
+    This migrator updates the dependency on `cutensor` to 2.x. Since 2.x has API
+    breaking changes, be sure your package has the latest support tested before
+    merging. Otherwise, please keep the PR open (and better, in draft status) as
+    instructed [here](https://conda-forge.org/docs/maintainer/knowledge_base.html#migrators-and-migrations)
+    until the package is ready to migrate.
 
 cutensor:
   - 2
diff --git a/recipe/meta.yaml b/recipe/meta.yaml
index 80544bdf..815f8dc0 100755
--- a/recipe/meta.yaml
+++ b/recipe/meta.yaml
@@ -1,7 +1,7 @@
 {% set name = "cupy" %}
 {% set version = "13.0.0" %}
 {% set sha256 = "2f04e7857f692a713360dc9c3b06709806ab8404fca39b5af9721c04a2979aae" %}
-{% set build_num = 1 %}
+{% set build_num = 2 %}
 
 {% set target_name = "x86_64-linux" %}  # [linux64]
 {% set target_name = "ppc64le-linux" %}  # [ppc64le]
@@ -57,6 +57,9 @@ outputs:
         - libcurand        # [(cuda_compiler_version or "").startswith("12")]
         - libcusolver      # [(cuda_compiler_version or "").startswith("12")]
         - libcusparse      # [(cuda_compiler_version or "").startswith("12")]
+        # see discussions/references in conda-forge/cupy-feedstock#247
+        - cuda-version >=12.0,<13.0a0  # [(cuda_compiler_version or "").startswith("12")]
+        - cuda-version >=11.0,<12.0a0  # [(cuda_compiler_version or "").startswith("11")]
     test:
       requires:
         # need the libcuda stub for import test