diff --git a/var/spack/repos/builtin/packages/datatransferkit/package.py b/var/spack/repos/builtin/packages/datatransferkit/package.py
index 8ac75863bb7..0274324d617 100644
--- a/var/spack/repos/builtin/packages/datatransferkit/package.py
+++ b/var/spack/repos/builtin/packages/datatransferkit/package.py
@@ -46,7 +46,7 @@ class Datatransferkit(CMakePackage):
     depends_on("trilinos+openmp", when="+openmp")
     depends_on("trilinos+stratimikos+belos", when="@master")
     depends_on("trilinos@13:13.4.1", when="@3.1-rc2:3.1-rc3")
-    depends_on("trilinos@14.2:", when="@3.1.0:")
+    depends_on("trilinos@14.2:16.0", when="@3.1.0:")
 
     def cmake_args(self):
         spec = self.spec
diff --git a/var/spack/repos/builtin/packages/trilinos/package.py b/var/spack/repos/builtin/packages/trilinos/package.py
index e1106ce4878..a405b31fd16 100644
--- a/var/spack/repos/builtin/packages/trilinos/package.py
+++ b/var/spack/repos/builtin/packages/trilinos/package.py
@@ -425,15 +425,15 @@ class Trilinos(CMakePackage, CudaPackage, ROCmPackage):
         depends_on("kokkos-kernels~shared", when="+cuda_rdc")
         depends_on("kokkos-kernels~shared", when="+rocm_rdc")
         depends_on("kokkos~complex_align")
-        depends_on("kokkos@4.5.01", when="@master:")
-        depends_on("kokkos@4.5.01", when="@16.1")
-        depends_on("kokkos@4.3.01", when="@16")
-        depends_on("kokkos@4.2.01", when="@15.1:15")
-        depends_on("kokkos@4.1.00", when="@14.4:15.0")
-        depends_on("kokkos-kernels@4.5.01", when="@master:")
-        depends_on("kokkos-kernels@4.5.01", when="@16.1")
-        depends_on("kokkos-kernels@4.3.01", when="@16")
-        depends_on("kokkos-kernels@4.2.01", when="@15.1:15")
+        depends_on("kokkos@=4.5.01", when="@master:")
+        depends_on("kokkos@=4.5.01", when="@16.1")
+        depends_on("kokkos@=4.3.01", when="@16.0")
+        depends_on("kokkos@=4.2.01", when="@15.1:15")
+        depends_on("kokkos@=4.1.00", when="@14.4:15.0")
+        depends_on("kokkos-kernels@=4.5.01", when="@master:")
+        depends_on("kokkos-kernels@=4.5.01", when="@16.1")
+        depends_on("kokkos-kernels@=4.3.01", when="@16.0")
+        depends_on("kokkos-kernels@=4.2.01", when="@15.1:15")
         depends_on("kokkos+openmp", when="+openmp")
 
         for a in CudaPackage.cuda_arch_values: