diff --git a/examples/diffusion/mesh1D.py b/examples/diffusion/mesh1D.py
index a9f8e71a4f..6c64b8a65d 100755
--- a/examples/diffusion/mesh1D.py
+++ b/examples/diffusion/mesh1D.py
@@ -720,24 +720,30 @@
 
 and solve the steady-state problem
 
->>> DiffusionTerm(coeff=D).solve(var=phi) #doctest: +PYSPARSE_SOLVER
+>>> try:
+...     DiffusionTerm(coeff=D).solve(var=phi)
+... except:
+...     pass
 >>> if __name__ == '__main__':
 ...     viewer.plot()
 >>> from fipy import input
 >>> if __name__ == '__main__':
-...     input("No-flux - stead-state failure. \
+...     input("No-flux - steady-state failure. \
 ... Press <return> to proceed...")
 
->>> print(numerix.allclose(phi, 0.0)) #doctest: +PYSPARSE_SOLVER
-True
+>>> print(numerix.allclose(phi, 0.2, atol=1e-5)) # doctest: +NOT_TRILINOS_SOLVER
+False
 
 .. image:: /figures/examples/diffusion/mesh1D-noflux_steady_fail.*
    :width: 90%
    :align: center
    :alt: (failed) steady-state solution for no-flux boundary conditions
 
-we find that the value is uniformly zero! What happened to our no-flux boundary
-conditions?
+Depending on the solver, we find that the value may be uniformly zero,
+infinity, or NaN, or the solver may just fail!
+What happened to our no-flux boundary conditions?
+Trilinos actually manages to get the correct solution, but this should not
+be relied on; this problem has an infinite number of solutions.
 
 The problem is that in the implicit discretization of :math:`\nabla\cdot(D\nabla\phi) = 0`,
 
diff --git a/fipy/solvers/__init__.py b/fipy/solvers/__init__.py
index 01180b9267..613e68b9ec 100644
--- a/fipy/solvers/__init__.py
+++ b/fipy/solvers/__init__.py
@@ -190,6 +190,12 @@ def _import_mesh_matrices(suite):
                  test=lambda: solver_suite != 'pyamgx',
                  why="the PyAMGX solver is being used.",
                  skipWarning=True)
+
+register_skipper(flag='NOT_TRILINOS_SOLVER',
+                 test=lambda: solver_suite not in ['trilinos', 'no-pysparse'],
+                 why="the Trilinos solvers are being used.",
+                 skipWarning=True)
+
 del register_skipper
 
 _log.info("Solver suite is %s", solver_suite)