diff --git a/conda/environments/cudf_dev_cuda11.0.yml b/conda/environments/cudf_dev_cuda11.0.yml
index a44472de7dc..171a5ed8af5 100644
--- a/conda/environments/cudf_dev_cuda11.0.yml
+++ b/conda/environments/cudf_dev_cuda11.0.yml
@@ -10,7 +10,7 @@ dependencies:
   - clang=8.0.1
   - clang-tools=8.0.1
   - cupy>7.1.0,<10.0.0a0
-  - rmm=0.20.*
+  - rmm=21.06.*
   - cmake>=3.18
   - cmake_setuptools>=0.1.3
   - python>=3.7,<3.9
@@ -44,7 +44,7 @@ dependencies:
   - dask==2021.4.0
   - distributed>=2.22.0,<=2021.4.0
   - streamz
-  - dlpack
+  - dlpack==0.3
   - arrow-cpp=1.0.1
   - arrow-cpp-proc * cuda
   - double-conversion
diff --git a/conda/environments/cudf_dev_cuda11.2.yml b/conda/environments/cudf_dev_cuda11.2.yml
index 6e8d3e58cf1..28373d203d1 100644
--- a/conda/environments/cudf_dev_cuda11.2.yml
+++ b/conda/environments/cudf_dev_cuda11.2.yml
@@ -10,7 +10,7 @@ dependencies:
   - clang=8.0.1
   - clang-tools=8.0.1
   - cupy>7.1.0,<10.0.0a0
-  - rmm=0.20.*
+  - rmm=21.06.*
   - cmake>=3.18
   - cmake_setuptools>=0.1.3
   - python>=3.7,<3.9
@@ -44,7 +44,7 @@ dependencies:
   - dask==2021.4.0
   - distributed>=2.22.0,<=2021.4.0
   - streamz
-  - dlpack
+  - dlpack==0.3
   - arrow-cpp=1.0.1
   - arrow-cpp-proc * cuda
   - double-conversion
diff --git a/conda/recipes/cudf/meta.yaml b/conda/recipes/cudf/meta.yaml
index eda11cde899..e0b37e97c9c 100644
--- a/conda/recipes/cudf/meta.yaml
+++ b/conda/recipes/cudf/meta.yaml
@@ -26,7 +26,7 @@ requirements:
     - cython >=0.29,<0.30
     - setuptools
     - numba >=0.53.1
-    - dlpack
+    - dlpack 0.3
     - pyarrow 1.0.1
     - libcudf {{ version }}
     - rmm {{ minor_version }}
diff --git a/conda/recipes/libcudf/meta.yaml b/conda/recipes/libcudf/meta.yaml
index 0b3fb5aa549..ea2fda399fd 100644
--- a/conda/recipes/libcudf/meta.yaml
+++ b/conda/recipes/libcudf/meta.yaml
@@ -39,7 +39,7 @@ requirements:
     - cudatoolkit {{ cuda_version }}.*
     - arrow-cpp 1.0.1
     - arrow-cpp-proc * cuda
-    - dlpack
+    - dlpack 0.3
   run:
     - {{ pin_compatible('cudatoolkit', max_pin='x.x') }}
     - arrow-cpp-proc * cuda
diff --git a/cpp/cmake/thirdparty/CUDF_GetRMM.cmake b/cpp/cmake/thirdparty/CUDF_GetRMM.cmake
index 9f6221d5d1f..b2861ae48c4 100644
--- a/cpp/cmake/thirdparty/CUDF_GetRMM.cmake
+++ b/cpp/cmake/thirdparty/CUDF_GetRMM.cmake
@@ -20,6 +20,12 @@ function(find_and_configure_rmm VERSION)
         return()
     endif()
 
+    if(${VERSION} MATCHES [=[([0-9]+)\.([0-9]+)\.([0-9]+)]=])
+        set(MAJOR_AND_MINOR "${CMAKE_MATCH_1}.${CMAKE_MATCH_2}")
+    else()
+        set(MAJOR_AND_MINOR "${VERSION}")
+    endif()
+
     # Consumers have two options for local source builds:
     # 1. Pass `-D CPM_rmm_SOURCE=/path/to/rmm` to build a local RMM source tree
     # 2. Pass `-D CMAKE_PREFIX_PATH=/path/to/rmm/build` to use an existing local
@@ -27,7 +33,7 @@ function(find_and_configure_rmm VERSION)
     CPMFindPackage(NAME rmm
         VERSION         ${VERSION}
         GIT_REPOSITORY  https://github.com/rapidsai/rmm.git
-        GIT_TAG         branch-${VERSION}
+        GIT_TAG         branch-${MAJOR_AND_MINOR}
         GIT_SHALLOW     TRUE
         OPTIONS         "BUILD_TESTS OFF"
                         "BUILD_BENCHMARKS OFF"
@@ -39,6 +45,6 @@ function(find_and_configure_rmm VERSION)
     fix_cmake_global_defaults(rmm::rmm)
 endfunction()
 
-set(CUDF_MIN_VERSION_rmm "${CUDF_VERSION_MAJOR}.${CUDF_VERSION_MINOR}")
+set(CUDF_MIN_VERSION_rmm "${CUDF_VERSION_MAJOR}.${CUDF_VERSION_MINOR}.00")
 
 find_and_configure_rmm(${CUDF_MIN_VERSION_rmm})