diff --git a/gtsam/linear/JacobianFactor.cpp b/gtsam/linear/JacobianFactor.cpp
index 56a5dc085..5cc626ffc 100644
--- a/gtsam/linear/JacobianFactor.cpp
+++ b/gtsam/linear/JacobianFactor.cpp
@@ -115,7 +115,7 @@ JacobianFactor::JacobianFactor(const HessianFactor& factor) :
   boost::tie(maxrank, success) = choleskyCareful(Ab_.matrix());
 
   // Check for indefinite system
-  if (!success)
+  if (!success and maxrank < factor.rows() - 1)
     throw IndeterminantLinearSystemException(factor.keys().front());
 
   // Zero out lower triangle
diff --git a/gtsam_unstable/linear/tests/testQPSolver.cpp b/gtsam_unstable/linear/tests/testQPSolver.cpp
index a5dde9951..2292c63d7 100644
--- a/gtsam_unstable/linear/tests/testQPSolver.cpp
+++ b/gtsam_unstable/linear/tests/testQPSolver.cpp
@@ -322,7 +322,7 @@ TEST(QPSolver, HS268) { // This test needs an extra order of magnitude of tolera
   CHECK(assert_equal(5.73107049e-07,error_actual, 1e-6))
 }
 
-TEST_DISABLED(QPSolver, QPTEST) { // REQUIRES Jacobian Fix
+TEST(QPSolver, QPTEST) { // REQUIRES Jacobian Fix
   QP problem = QPSParser("QPTEST.QPS").Parse();
   VectorValues actualSolution;
   boost::tie(actualSolution, boost::tuples::ignore) = QPSolver(problem).optimize();