diff --git a/.github/workflows/conda.yml b/.github/workflows/conda.yml
index e6e2fb379..33f7d6f63 100644
--- a/.github/workflows/conda.yml
+++ b/.github/workflows/conda.yml
@@ -27,17 +27,15 @@ jobs:
     strategy:
       fail-fast: false
       matrix:
-        include:
-          # We use the oldest ubuntu available to have forward compatibility of the libc
-          - os: ubuntu-20.04
-            os-family: linux-64
-          - os: windows-2022
-            os-family: win-64
-          - os: macos-13
-            os-family: osx-64
-          - os: macos-14
-            os-family: osx-arm64
-    runs-on: ${{ matrix.os }}
+        env:
+          # Linux: We use the manylinux container to be compatible with libc >= 2.28
+          - {os: ubuntu-22.04, os-family: linux-64, json-image: '{"image": "ubuntu:18.10"}'}
+          - {os: ubuntu-22.04, os-family: linux-64, json-image: '{"image": null}'}
+          - {os: windows-2022, os-family: win-64, json-image: '{"image": null}'}
+          - {os: macos-13, os-family: osx-64, json-image: '{"image": null}'}
+          - {os: macos-14, os-family: osx-arm64, json-image: '{"image": null}'}
+    runs-on: ${{ matrix.env.os }}
+    container: ${{ fromJSON(matrix.env.json-image) }}
     steps:
       - name: Checkout Sources
         uses: actions/checkout@v4
@@ -68,17 +66,23 @@ jobs:
 
           # The conda version cannot have '-' as a character so we eliminate it
           echo "KHIOPS_VERSION=$(echo $KHIOPS_RAW_VERSION | sed 's/-//')" >> "$GITHUB_ENV"
-      - name: Build conda packages (Windows)
+      - name: Install g++ for Linux Docker
+        if: contains(fromJSON(matrix.env.json-image), 'ubuntu')
+        run: |
+          sudo apt-get -y update
+          sudo apt-get -y install g++
+          which g++
+      - name: Build Conda Package (Windows)
         if: runner.os == 'Windows'
         run: conda build --output-folder ./build/conda ./packaging/conda
       # In Linux/macOS we need the conda-forge channel to install their pinned versions
-      - name: Build conda packages (Linux/macOS)
+      - name: Build Conda Package (Linux/macOS)
         if: runner.os != 'Windows'
         run: conda build --channel conda-forge --output-folder ./build/conda ./packaging/conda
       - name: Upload conda packages artifact
         uses: actions/upload-artifact@v4
         with:
-          name: khiops-conda-${{ matrix.os-family }}
+          name: khiops-conda-${{ matrix.env.os-family }}
           path: ./build/conda
           retention-days: 7
   # Test Conda package on brand new environments
diff --git a/packaging/conda/build.sh b/packaging/conda/build.sh
index 85a4d1174..7026b815a 100644
--- a/packaging/conda/build.sh
+++ b/packaging/conda/build.sh
@@ -3,21 +3,35 @@
 # Set-up the shell to behave more like a general-purpose programming language
 set -euo pipefail
 
+ls "$PREFIX/bin"
+
 # Choose the build preset for macOS/Linux
-if [[ "$(uname)" == "Darwin" ]]
+if [[ "$(uname)" == "Linux" ]]
 then
-  CMAKE_PRESET="macos-clang-release"
-else
   CMAKE_PRESET="linux-gcc-release"
+  cmake --fresh --preset $CMAKE_PRESET -DBUILD_JARS=OFF -DTESTING=OFF -DMPI_SUFFIX=_openmpi
+else
+  CMAKE_PRESET="macos-clang-release"
+  cmake --fresh --preset $CMAKE_PRESET -DBUILD_JARS=OFF -DTESTING=OFF
 fi
 
 # Build MODL and MODL_Coclustering
-cmake --fresh --preset $CMAKE_PRESET -DBUILD_JARS=OFF -DTESTING=OFF
 cmake --build --preset $CMAKE_PRESET --parallel --target MODL MODL_Coclustering
 
 # Copy the MODL binaries to the Conda PREFIX path
-cp "./build/$CMAKE_PRESET/bin/MODL" "$PREFIX/bin"
-cp "./build/$CMAKE_PRESET/bin/MODL_Coclustering" "$PREFIX/bin"
+ls -ltr "./build/$CMAKE_PRESET/bin"
+mv ./build/$CMAKE_PRESET/bin/MODL* "$PREFIX/bin"
+
+# Rename MODL in Linux since it has a prefix depending of the MPI version
+if [[ "$(uname)" == "Linux" ]]
+then
+  if [[ -f "$PREFIX/bin/MODL_mpich" ]]
+  then
+    mv "$PREFIX/bin/MODL_mpich" "$PREFIX/bin/MODL"
+  else
+    mv "$PREFIX/bin/MODL_openmpi" "$PREFIX/bin/MODL"
+  fi
+fi
 
 # Custom rpath relocation and signing executables for macOS in arm64
 #
diff --git a/packaging/conda/conda_build_config.yaml b/packaging/conda/conda_build_config.yaml
index 03d8c9e6a..6eab5c0b3 100644
--- a/packaging/conda/conda_build_config.yaml
+++ b/packaging/conda/conda_build_config.yaml
@@ -1,4 +1,7 @@
 ---
+mpi:
+  - openmpi=4.1.6  # [not win]
+  - msmpi  # [win]
 # We need MacOS SDK 10.10 to be able to build on macOS Intel
 # Download: https://github.com/phracker/MacOSX-SDKs/releases/download/11.3/MacOSX10.10.sdk.tar.xz
 # Decompress then to /opt: tar -zxvf MacOSX10.10.sdk.tar.xz -C /opt
diff --git a/packaging/conda/meta.yaml b/packaging/conda/meta.yaml
index 662716986..fb67323dd 100644
--- a/packaging/conda/meta.yaml
+++ b/packaging/conda/meta.yaml
@@ -26,35 +26,17 @@ build:
   detect_binary_files_with_prefix: false # [osx]
   {% endif %}
 
-# Note on version pinning:
-# OSX:
-# - mpich=3.4.3 because 4.* is still unstable
-# - requires conda-forge
-# Linux:
-# - mpich=4.0.3 because of bugs of the 3.* series
-# - requires conda-forge
 requirements:
   build:
-    - mpich 4.0.3        # [linux]
-    - mpich-mpicc  4.0.3 # [linux]
-    - mpich-mpicxx 4.0.3 # [linux]
-    - mpich 3.4.3        # [osx]
-    - mpich-mpicc  3.4.3 # [osx]
-    - mpich-mpicxx 3.4.3 # [osx]
-    - msmpi              # [win]
     - cmake
     - ninja
     - {{ compiler('cxx') }}
   host:
-    - mpich 4.0.3        # [linux]
-    - mpich-mpicxx 4.0.3 # [linux]
-    - mpich 3.4.3        # [osx]
-    - mpich-mpicxx 3.4.3 # [osx]
-    - msmpi              # [win]
+    - {{ mpi }}
+    - openssh  # [linux]
   run:
-    - mpich 4.0.3   # [linux]
-    - mpich 3.4.3   # [osx]
-    - msmpi         # [win]
+    - {{ mpi }}
+    - openssh  # [linux]
 
 outputs:
   - name: khiops-core