diff --git a/internal/ceres/suitesparse.cc b/internal/ceres/suitesparse.cc
index e108ec694..189a24f02 100644
--- a/internal/ceres/suitesparse.cc
+++ b/internal/ceres/suitesparse.cc
@@ -165,6 +165,13 @@ cholmod_factor* SuiteSparse::AnalyzeCholesky(cholmod_sparse* A,
                                              std::string* message) {
   cc_.nmethods = 1;
   cc_.method[0].ordering = OrderingTypeToCHOLMODEnum(ordering_type);
+
+  // postordering with a NATURAL ordering leads to a significant regression in
+  // performance. See https://github.com/ceres-solver/ceres-solver/issues/905
+  if (ordering_type == OrderingType::NATURAL) {
+    cc_.postorder = 0;
+  }
+
   cholmod_factor* factor = cholmod_analyze(A, &cc_);
 
   if (cc_.status != CHOLMOD_OK) {