diff --git a/.github/workflows/bleeding-edge.yml b/.github/workflows/bleeding-edge.yml
index f79720fbf..17527a1eb 100644
--- a/.github/workflows/bleeding-edge.yml
+++ b/.github/workflows/bleeding-edge.yml
@@ -46,10 +46,7 @@ jobs:
         run: sudo apt-get install libglu1-mesa-dev
       - name: Install build dependencies
         run: |
-          sudo apt-get install swig
-          python -m pip install -U pip setuptools wheel
-          python -m pip install numpy
-          python -m pip install Cython
+          python -m pip install -U pip wheel
       - name: Install prebuilt wxPython
         run: python -m pip install -f https://extras.wxpython.org/wxPython4/extras/linux/gtk3/ubuntu-18.04 wxPython
         if: matrix.toolkit == 'wx'
diff --git a/ci/edmtool.py b/ci/edmtool.py
index 8f75f84f2..2aa921e9c 100644
--- a/ci/edmtool.py
+++ b/ci/edmtool.py
@@ -104,9 +104,9 @@
         "pyparsing",
         "pypdf2",
         "reportlab",
-        "swig",
         "traits",
         "traitsui",
+        "wheel",
     },
     '3.8': {
         "apptools",
@@ -120,9 +120,9 @@
         "pyface",
         "pygments",
         "pyparsing",
-        "swig",
         "traits",
         "traitsui",
+        "wheel",
     }
 }
 
diff --git a/pyproject.toml b/pyproject.toml
index 42eecc8f0..54d49e451 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -1,3 +1,3 @@
 [build-system]
-requires = ["cython", "oldest-supported-numpy", "setuptools", "wheel"]
+requires = ["cython", "oldest-supported-numpy", "setuptools", "swig", "wheel"]
 build-backend = "setuptools.build_meta"
diff --git a/setup.py b/setup.py
index 6499ad036..98cb9cd33 100644
--- a/setup.py
+++ b/setup.py
@@ -428,21 +428,8 @@ def macos_extensions():
     ]
 
 
-def verify_swig_install():
-    """ Verify that SWIG is installed.
-    """
-    msg = ("SWIG is a required build dependency of Enable. Please install "
-           "SWIG (see http://www.swig.org/).")
-    try:
-        subprocess.run(["swig", "-version"], check=True)
-    except (FileNotFoundError, subprocess.CalledProcessError):
-        raise Exception(msg)
-
-
 if __name__ == "__main__":
 
-    verify_swig_install()
-
     # Write version modules as needed
     enable_version_path = os.path.join('enable', '_version.py')
     write_version_py(filename=enable_version_path)