diff --git a/.github/workflows/docker-bases.yml b/.github/workflows/docker-bases.yml
index f0574af99b3..2d10b3e7e8c 100644
--- a/.github/workflows/docker-bases.yml
+++ b/.github/workflows/docker-bases.yml
@@ -72,12 +72,6 @@ jobs:
             dockerfile: './docker/Dockerfile.cpu'
             runner: ubuntu-latest 
 
-          - tag: 'devitocodes/bases:cpu-icx'
-            arch: 'arch=icx'
-            version: ''
-            dockerfile: './docker/Dockerfile.cpu'
-            runner: ubuntu-latest
-
           - tag: 'devitocodes/bases:cpu-nvc'
             arch: 'arch=nvc-host'
             version: ''
diff --git a/.github/workflows/pytest-core-nompi.yml b/.github/workflows/pytest-core-nompi.yml
index d08386ee95b..c59628b12ff 100644
--- a/.github/workflows/pytest-core-nompi.yml
+++ b/.github/workflows/pytest-core-nompi.yml
@@ -34,8 +34,8 @@ jobs:
            pytest-ubuntu-py39-gcc9-omp,
            pytest-osx-py37-clang-omp,
            pytest-docker-py37-gcc-omp,
-           pytest-docker-py37-icc-omp,
-           pytest-docker-py38-icx-omp
+           pytest-docker-py37-intel-omp,
+           pytest-docker-py38-intel-omp
         ]
         set: [base, adjoint]
         include:
@@ -95,14 +95,14 @@ jobs:
           language: "openmp"
           sympy: "1.10"
 
-        - name: pytest-docker-py37-icc-omp
+        - name: pytest-docker-py37-intel-omp
           python-version: '3.7'
           os: ubuntu-22.04
           arch: "icc"
           language: "openmp"
           sympy: "1.11"
 
-        - name: pytest-docker-py38-icx-omp
+        - name: pytest-docker-py38-intel-omp
           python-version: '3.8'
           os: ubuntu-22.04
           arch: "icx"
@@ -129,15 +129,20 @@ jobs:
       with:
         python-version: ${{ matrix.python-version }}
 
-    - name: Build docker image
-      if: contains(matrix.name, 'docker')
+    - name: Build docker image for GCC variants
+      if: "contains(matrix.name, 'docker') && contains(matrix.name, 'gcc')"
       run: |
           docker build . --file docker/Dockerfile.devito --tag devito_img --build-arg base=devitocodes/bases:cpu-${{ matrix.arch }}
 
+    - name: Build docker image for INTEL variants
+      if: "contains(matrix.name, 'docker') && contains(matrix.name, 'intel')"
+      run: |
+          docker build . --file docker/Dockerfile.devito --tag devito_img --build-arg base=devitocodes/bases:cpu-icc
+
     - name: Set run prefix
       run: |
           if [[ "${{ matrix.name }}" =~ "docker" ]]; then
-              echo "RUN_CMD=docker run --rm -e CODECOV_TOKEN=${{ secrets.CODECOV_TOKEN }} --name testrun devito_img"  >> $GITHUB_ENV
+              echo "RUN_CMD=docker run --rm -e CODECOV_TOKEN=${{ secrets.CODECOV_TOKEN }} -e DEVITO_ARCH=${{ matrix.arch }} --name testrun devito_img"  >> $GITHUB_ENV
           else
               echo "RUN_CMD=" >> $GITHUB_ENV
           fi
diff --git a/devito/arch/compiler.py b/devito/arch/compiler.py
index b17de06d685..86c6e85e124 100644
--- a/devito/arch/compiler.py
+++ b/devito/arch/compiler.py
@@ -552,8 +552,8 @@ def __init__(self, *args, **kwargs):
                 self.cflags.append('-fsycl-targets=spir64')
 
         if language == 'openmp':
-            # To be switched to `-fiopenmp` or `-qopenmp` as soon as
-            # it is fixed in the new Intel OneAPI release
+            # TODO: To be switched to `-fiopenmp` or `-qopenmp` as soon as
+            # it is fixed in the new Intel OneAPI release (current: 2023.0)
             self.cflags.append('-fopenmp')
             if platform is NVIDIAX:
                 self.cflags.append('-fopenmp-targets=nvptx64-cuda')
@@ -854,11 +854,11 @@ def __lookup_cmds__(self):
     'nvidia': NvidiaCompiler,
     'cuda': CudaCompiler,
     'osx': ClangCompiler,
-    'intel': IntelCompiler,
-    'icpc': IntelCompiler,
-    'icc': IntelCompiler,
+    'intel': OneapiCompiler,
     'icx': OneapiCompiler,
     'icpx': OneapiCompiler,
+    'icc': IntelCompiler,
+    'icpc': IntelCompiler,
     'intel-knl': IntelKNLCompiler,
     'knl': IntelKNLCompiler,
     'dpcpp': DPCPPCompiler,
diff --git a/devito/parameters.py b/devito/parameters.py
index 0c56f10b441..fab69407609 100644
--- a/devito/parameters.py
+++ b/devito/parameters.py
@@ -241,6 +241,13 @@ def __init__(self, **params):
     def __call__(self, func, *args, **kwargs):
         @wraps(func)
         def wrapper(*args, **kwargs):
+            # Do not switch if condition is False
+            try:
+                if not self.params.pop('condition'):
+                    return
+            except KeyError:
+                pass
+
             previous = {}
             for k, v in self.params.items():
                 previous[k] = configuration[k]
diff --git a/docker/Dockerfile.cpu b/docker/Dockerfile.cpu
index 5a4a6ee234a..9ebda2d9f0c 100644
--- a/docker/Dockerfile.cpu
+++ b/docker/Dockerfile.cpu
@@ -55,14 +55,6 @@ ENV DEVITO_LANGUAGE="openmp"
 # MPICC compiler for mpi4py
 ENV MPICC=$I_MPI_ROOT/bin/mpiicc
 
-##############################################################
-# ICX image
-##############################################################
-FROM icc as icx
-
-# Devito config
-ENV DEVITO_ARCH="icx"
-
 ##############################################################
 # Published image
 ##############################################################
diff --git a/tests/conftest.py b/tests/conftest.py
index 5c8c16fdeb7..51d8e631383 100644
--- a/tests/conftest.py
+++ b/tests/conftest.py
@@ -7,8 +7,7 @@
 from devito import Eq, configuration  # noqa
 from devito.finite_differences.differentiable import EvalDerivative
 from devito.arch import Cpu64, Device, sniff_mpi_distro, Arm
-from devito.arch.compiler import (compiler_registry, IntelCompiler, OneapiCompiler,
-                                  NvidiaCompiler)
+from devito.arch.compiler import compiler_registry, IntelCompiler, NvidiaCompiler
 from devito.ir.iet import retrieve_iteration_tree, FindNodes, Iteration, ParallelBlock
 from devito.tools import as_tuple
 
@@ -24,8 +23,7 @@ def skipif(items, whole_module=False):
     # Sanity check
     accepted = set()
     accepted.update({'device', 'device-C', 'device-openmp', 'device-openacc',
-                     'device-aomp', 'cpu64-icc', 'cpu64-icpx', 'cpu64-nvc',
-                     'cpu64-arm'})
+                     'device-aomp', 'cpu64-icc', 'cpu64-nvc', 'cpu64-arm'})
     accepted.update({'nompi', 'nodevice'})
     unknown = sorted(set(items) - accepted)
     if unknown:
@@ -71,12 +69,6 @@ def skipif(items, whole_module=False):
            isinstance(configuration['platform'], Cpu64):
             skipit = "`icc+cpu64` won't work with this test"
             break
-        # Skip if it won't run with OneAPICompiler
-        if i == 'cpu64-icpx' and \
-           isinstance(configuration['compiler'], OneapiCompiler) and \
-           isinstance(configuration['platform'], Cpu64):
-            skipit = "`icpx+cpu64` won't work with this test"
-            break
         # Skip if it won't run on Arm
         if i == 'cpu64-arm' and isinstance(configuration['platform'], Arm):
             skipit = "Arm doesn't support x86-specific instructions"
diff --git a/tests/test_dimension.py b/tests/test_dimension.py
index f38a8e18b84..af2a8bb7538 100644
--- a/tests/test_dimension.py
+++ b/tests/test_dimension.py
@@ -9,7 +9,8 @@
                     SparseFunction, SparseTimeFunction, Eq, Operator, Constant,
                     Dimension, DefaultDimension, SubDimension, switchconfig,
                     SubDomain, Lt, Le, Gt, Ge, Ne, Buffer, sin, SpaceDimension,
-                    CustomDimension, dimensions)
+                    CustomDimension, dimensions, configuration)
+from devito.arch.compiler import OneapiCompiler
 from devito.ir.iet import (Conditional, Expression, Iteration, FindNodes,
                            FindSymbols, retrieve_iteration_tree)
 from devito.symbolics import indexify, retrieve_functions, IntDiv
@@ -1382,8 +1383,8 @@ def test_affiness(self):
         iterations = [i for i in FindNodes(Iteration).visit(op) if i.dim is not time]
         assert all(i.is_Affine for i in iterations)
 
-    # Skipping this test with icx, as it requires safe-math
-    @skipif('cpu64-icpx')
+    @switchconfig(condition=isinstance(configuration['compiler'],
+                  OneapiCompiler), safe_math=True)
     def test_sparse_time_function(self):
         nt = 20