diff --git a/var/spack/repos/builtin/packages/mgis/package.py b/var/spack/repos/builtin/packages/mgis/package.py
index 545ed49dc9e..d345d7476ff 100644
--- a/var/spack/repos/builtin/packages/mgis/package.py
+++ b/var/spack/repos/builtin/packages/mgis/package.py
@@ -70,6 +70,7 @@ class Mgis(CMakePackage):
     depends_on("tfel@3.3.0", when="@1.1")
     depends_on("tfel@3.2.1", when="@1.0.1")
     depends_on("tfel@3.2.0", when="@1.0")
+    depends_on("tfel@rliv-5.0", when="@rliv-3.0")
     depends_on("tfel@rliv-4.2", when="@rliv-2.2")
     depends_on("tfel@rliv-4.1", when="@rliv-2.1")
     depends_on("tfel@rliv-4.0", when="@rliv-2.0")
@@ -77,11 +78,22 @@ class Mgis(CMakePackage):
     depends_on("tfel@rliv-3.3", when="@rliv-1.1")
     depends_on("tfel@rliv-3.2", when="@rliv-1.0")
     depends_on("tfel@master", when="@master")
-    depends_on(
-        "boost+python+numpy+exception+container", when="+python", type=("build", "link", "run")
-    )
+
     depends_on("py-numpy", when="+python", type=("build", "link", "run"))
 
+    with when("@3.1:"):
+        depends_on("py-pybind11", when="+python", type=("build", "link", "run"))
+
+    with when("@1.0:3.0.99"):
+        depends_on(
+            "boost+python+numpy+exception+container", when="+python", type=("build", "link", "run")
+        )
+
+    with when("@rliv-1.0:rliv-3.0"):
+        depends_on(
+            "boost+python+numpy+exception+container", when="+python", type=("build", "link", "run")
+        )
+
     extends("python", when="+python")
 
     def patch(self):
@@ -113,8 +125,13 @@ def cmake_args(self):
             args.append("-DPYTHON_LIBRARY={0}".format(python.libs[0]))
             args.append("-DPYTHON_INCLUDE_DIR={0}".format(python.headers.directories[0]))
             args.append("-DPython_ADDITIONAL_VERSIONS={0}".format(python.version.up_to(2)))
-            # adding path to boost
-            args.append("-DBOOST_ROOT={0}".format(self.spec["boost"].prefix))
+
+            if "py-pybind11" in self.spec:
+                args.append("-Dpybind11_DIR={0}".format(self.spec["py-pybind11"].prefix))
+
+            if "boost" in self.spec:
+                # adding path to boost
+                args.append("-DBOOST_ROOT={0}".format(self.spec["boost"].prefix))
 
         if "+static" in self.spec:
             args.append("-Denable-static=ON")
diff --git a/var/spack/repos/builtin/packages/tfel/package.py b/var/spack/repos/builtin/packages/tfel/package.py
index 183a477cb04..707db1f8b5f 100644
--- a/var/spack/repos/builtin/packages/tfel/package.py
+++ b/var/spack/repos/builtin/packages/tfel/package.py
@@ -26,7 +26,7 @@ class Tfel(CMakePackage):
     constraints on each component of the strain or the stress.
     """
 
-    homepage = "https://tfel.sourceforge.net"
+    homepage = "https://thelfer.github.io/tfel/web/index.html"
     url = "https://github.com/thelfer/tfel/archive/TFEL-4.0.tar.gz"
     git = "https://github.com/thelfer/tfel.git"
     maintainers("thelfer")
@@ -155,12 +155,22 @@ class Tfel(CMakePackage):
     depends_on("python", when="+python_bindings", type=("build", "link", "run"))
     depends_on("py-numpy", when="+python_bindings", type=("build", "link", "run"))
 
-    # As boost+py has py runtime dependency, boost+py needs types link and run as well:
-    depends_on(
-        "boost+python+numpy+exception+container",
-        when="+python_bindings",
-        type=("build", "link", "run"),
-    )
+    with when("@5.1:"):
+        depends_on("py-pybind11", when="+python_bindings", type=("build", "link", "run"))
+
+    with when("@2.0.4:5.0.99"):
+        depends_on(
+            "boost+python+numpy+exception+container",
+            when="+python_bindings",
+            type=("build", "link", "run"),
+        )
+
+    with when("@rliv1.2:rliv5.0"):
+        depends_on(
+            "boost+python+numpy+exception+container",
+            when="+python_bindings",
+            type=("build", "link", "run"),
+        )
 
     extends("python", when="+python_bindings")
 
@@ -209,9 +219,14 @@ def cmake_args(self):
             args.append("-DPython_ADDITIONAL_VERSIONS={0}".format(python.version.up_to(2)))
 
         if "+python_bindings" in self.spec:
-            args.append("-DBOOST_ROOT={0}".format(self.spec["boost"].prefix))
-            args.append("-DBoost_NO_SYSTEM_PATHS=ON")
-            args.append("-DBoost_NO_BOOST_CMAKE=ON")
+
+            if "py-pybind11" in self.spec:
+                args.append("-Dpybind11_DIR={0}".format(self.spec["py-pybind11"].prefix))
+
+            if "boost" in self.spec:
+                args.append("-DBOOST_ROOT={0}".format(self.spec["boost"].prefix))
+                args.append("-DBoost_NO_SYSTEM_PATHS=ON")
+                args.append("-DBoost_NO_BOOST_CMAKE=ON")
 
         return args