diff --git a/conda/README.md b/conda/README.md
index 7b2594e07..4c1b719f6 100644
--- a/conda/README.md
+++ b/conda/README.md
@@ -24,7 +24,6 @@ docker run --rm -it \
     -e DESIRED_PYTHON=3.8 \
     -e PYTORCH_BUILD_VERSION=1.5.0 \
     -e PYTORCH_BUILD_NUMBER=1 \
-    -e OVERRIDE_PACKAGE_VERSION=1.5.0
     -e TORCH_CONDA_BUILD_FOLDER=pytorch-nightly \
     -v /path/to/pytorch:/pytorch \
     -v /path/to/builder:/builder \
diff --git a/conda/build_pytorch.sh b/conda/build_pytorch.sh
index 972b1acf5..3a0418191 100755
--- a/conda/build_pytorch.sh
+++ b/conda/build_pytorch.sh
@@ -254,13 +254,12 @@ if [[ -n "$cpu_only" ]]; then
     if [[ "$OSTYPE" != "darwin"* ]]; then
         build_string_suffix="cpu_${build_string_suffix}"
     fi
-    # on Linux, advertise that the package sets the cpuonly feature
-    export CONDA_CPU_ONLY_FEATURE="    - cpuonly # [not osx]"
+    export PYTORCH_BUILD_VARIANT="cpu"
 else
     # Switch the CUDA version that /usr/local/cuda points to. This script also
     # sets CUDA_VERSION and CUDNN_VERSION
     echo "Switching to CUDA version $desired_cuda"
-    export CONDA_CPU_ONLY_FEATURE=""
+    export PYTORCH_BUILD_VARIANT="cuda"
     . ./switch_cuda_version.sh "$desired_cuda"
     # TODO, simplify after anaconda fixes their cudatoolkit versioning inconsistency.
     # see: https://github.com/conda-forge/conda-forge.github.io/issues/687#issuecomment-460086164
diff --git a/conda/cpuonly/meta.yaml b/conda/cpuonly/meta.yaml
index c158aaf5c..c7d5a54dc 100644
--- a/conda/cpuonly/meta.yaml
+++ b/conda/cpuonly/meta.yaml
@@ -1,8 +1,12 @@
 package:
   name: cpuonly
-  version: 1.0
+  version: 2.0
 
 build:
   track_features:
       - cpuonly
   noarch: generic
+
+requirements:
+  run:
+    - pytorch-mutex 1.0 cpu
diff --git a/conda/pytorch-mutex/conda_build_config.yaml b/conda/pytorch-mutex/conda_build_config.yaml
new file mode 100644
index 000000000..e18e53eb4
--- /dev/null
+++ b/conda/pytorch-mutex/conda_build_config.yaml
@@ -0,0 +1,3 @@
+build_variant:
+    - cpu
+    - cuda
diff --git a/conda/pytorch-mutex/meta.yaml b/conda/pytorch-mutex/meta.yaml
new file mode 100644
index 000000000..fa7f916ec
--- /dev/null
+++ b/conda/pytorch-mutex/meta.yaml
@@ -0,0 +1,29 @@
+{% set version = "1.0" %}
+{% set build = 0 %}
+
+{% if build_variant == 'cuda' %}
+# prefer cuda builds via a build number offset
+{% set build = build + 100 %}
+{% endif %}
+
+package:
+  name: pytorch-mutex
+  version: {{ version }}
+build:
+  number: {{ build }}
+  string: {{ build_variant }}
+  noarch: generic
+  # also lower cpu priority with track_features
+  {% if build_variant == 'cpu' %}
+  track_features:
+      - pytorch-mutex
+  {% endif %}
+  run_exports:
+    - {{ pin_subpackage('pytorch-mutex', exact=True) }}
+requirements: {}
+  # None, pytorch should depend on pytorch-mutex
+test:
+  commands:
+    - echo "pytorch-mutex metapackage is created."
+about:
+  summary: Metapackage to select the PyTorch variant. Use conda's pinning mechanism in your environment to control which variant you want.
diff --git a/conda/pytorch-nightly/meta.yaml b/conda/pytorch-nightly/meta.yaml
index ec5075035..a24781ed1 100644
--- a/conda/pytorch-nightly/meta.yaml
+++ b/conda/pytorch-nightly/meta.yaml
@@ -1,3 +1,5 @@
+{% set build_variant = environ.get('PYTORCH_BUILD_VARIANT', 'cuda') %}
+
 package:
   name: pytorch
   version: "{{ environ.get('PYTORCH_BUILD_VERSION') }}"
@@ -36,8 +38,17 @@ requirements:
     - intel-openmp # [win]
     - typing_extensions
     - blas * mkl
+    - pytorch-mutex 1.0 {{ build_variant }}
 {{ environ.get('CONDA_CUDATOOLKIT_CONSTRAINT', '') }}
 
+  {% if build_variant == 'cpu' %}
+  run_constrained:
+    - cpuonly
+  {% else %}
+  run_constrained:
+     - cpuonly <0
+  {% endif %}
+
 build:
   number: {{ environ.get('PYTORCH_BUILD_NUMBER', '1') }}
   detect_binary_files_with_prefix: False