diff --git a/internal/ceres/iterative_schur_complement_solver.cc b/internal/ceres/iterative_schur_complement_solver.cc
index 0b1cb89..1aac565 100644
--- a/internal/ceres/iterative_schur_complement_solver.cc
+++ b/internal/ceres/iterative_schur_complement_solver.cc
@@ -78,6 +78,17 @@
   }
   schur_complement_->Init(*A, per_solve_options.D, b);
 
+  const int num_schur_complement_blocks =
+      A->block_structure()->cols.size() - options_.elimination_groups[0];
+  if (num_schur_complement_blocks == 0) {
+    VLOG(2) << "No parameter blocks left in the schur complement.";
+    LinearSolver::Summary cg_summary;
+    cg_summary.num_iterations = 0;
+    cg_summary.termination_type = TOLERANCE;
+    schur_complement_->BackSubstitute(NULL, x);
+    return cg_summary;
+  }
+
   // Initialize the solution to the Schur complement system to zero.
   //
   // TODO(sameeragarwal): There maybe a better initialization than an
@@ -116,16 +127,16 @@
     case SCHUR_JACOBI:
       if (preconditioner_.get() == NULL) {
         preconditioner_.reset(
-            new SchurJacobiPreconditioner(
-                *A->block_structure(), preconditioner_options));
+            new SchurJacobiPreconditioner(*A->block_structure(),
+                                          preconditioner_options));
       }
       break;
     case CLUSTER_JACOBI:
     case CLUSTER_TRIDIAGONAL:
       if (preconditioner_.get() == NULL) {
         preconditioner_.reset(
-            new VisibilityBasedPreconditioner(
-                *A->block_structure(), preconditioner_options));
+            new VisibilityBasedPreconditioner(*A->block_structure(),
+                                              preconditioner_options));
       }
       break;
     default:
diff --git a/internal/ceres/iterative_schur_complement_solver_test.cc b/internal/ceres/iterative_schur_complement_solver_test.cc
index 86e7825..db45741 100644
--- a/internal/ceres/iterative_schur_complement_solver_test.cc
+++ b/internal/ceres/iterative_schur_complement_solver_test.cc
@@ -58,9 +58,9 @@
 
 class IterativeSchurComplementSolverTest : public ::testing::Test {
  protected :
-  virtual void SetUp() {
+  void SetUpProblem(int problem_id) {
     scoped_ptr<LinearLeastSquaresProblem> problem(
-        CreateLinearLeastSquaresProblemFromId(2));
+        CreateLinearLeastSquaresProblemFromId(problem_id));
 
     CHECK_NOTNULL(problem.get());
     A_.reset(down_cast<BlockSparseMatrix*>(problem->A.release()));
@@ -90,7 +90,9 @@
     qr->Solve(&dense_A, b_.get(), per_solve_options, reference_solution.data());
 
     options.elimination_groups.push_back(num_eliminate_blocks_);
+    options.elimination_groups.push_back(0);
     options.max_num_iterations = num_cols_;
+    options.preconditioner_type = SCHUR_JACOBI;
     IterativeSchurComplementSolver isc(options);
 
     Vector isc_sol(num_cols_);
@@ -114,7 +116,14 @@
   scoped_array<double> D_;
 };
 
-TEST_F(IterativeSchurComplementSolverTest, SolverTest) {
+TEST_F(IterativeSchurComplementSolverTest, NormalProblem) {
+  SetUpProblem(2);
+  EXPECT_TRUE(TestSolver(NULL));
+  EXPECT_TRUE(TestSolver(D_.get()));
+}
+
+TEST_F(IterativeSchurComplementSolverTest, ProblemWithNoFBlocks) {
+  SetUpProblem(3);
   EXPECT_TRUE(TestSolver(NULL));
   EXPECT_TRUE(TestSolver(D_.get()));
 }