diff --git a/cblas.h b/cblas.h
index 8395f1b8b2..068fb34bde 100644
--- a/cblas.h
+++ b/cblas.h
@@ -40,6 +40,8 @@ extern "C" {
 /*Set the number of threads on runtime.*/
 void openblas_set_num_threads(int num_threads);
 void goto_set_num_threads(int num_threads);
+// "Local" means this number is used when OpenBLAS notices that
+// it is already in an OpenMP parallel region (`omp_in_parallel()`).
 int openblas_set_num_threads_local(int num_threads);
 
 /*Get the number of threads on runtime.*/
diff --git a/common_thread.h b/common_thread.h
index 4a8db682bf..3d34ebafe2 100644
--- a/common_thread.h
+++ b/common_thread.h
@@ -138,31 +138,30 @@ typedef struct blas_queue {
 extern int blas_server_avail;
 extern int blas_omp_number_max;
 extern int blas_omp_threads_local;
+extern int blas_is_num_threads_set_explicitly;
 
 static __inline int num_cpu_avail(int level) {
 
 #ifdef USE_OPENMP
-int openmp_nthreads;
-	openmp_nthreads=omp_get_max_threads();
-	if (omp_in_parallel()) openmp_nthreads = blas_omp_threads_local;
-#endif
+  /* If the user explicitly called openblas_set_num_threads(),
+     respect that setting instead of overriding it with
+     `omp_get_max_threads()` below (which is to get a default
+     in case the user hasn't made an explicit choice). */
+  if (blas_is_num_threads_set_explicitly) {
+    return blas_cpu_number;
+  }
 
-#ifndef USE_OPENMP 
-  if (blas_cpu_number == 1
-#else
-     if (openmp_nthreads == 1 
-#endif
-      ) return 1;        
+  int openmp_nthreads = omp_in_parallel() ? blas_omp_threads_local : omp_get_max_threads();
 
-#ifdef USE_OPENMP
-     if (openmp_nthreads > blas_omp_number_max){
+  if (openmp_nthreads > blas_omp_number_max) {
 #ifdef DEBUG
-     fprintf(stderr,"WARNING - more OpenMP threads requested (%d) than available (%d)\n",openmp_nthreads,blas_omp_number_max);
+    fprintf(stderr, "WARNING - more OpenMP threads requested (%d) than available (%d)\n", openmp_nthreads, blas_omp_number_max);
 #endif
-     openmp_nthreads = blas_omp_number_max;
-     }
-     if (blas_cpu_number != openmp_nthreads) {
-	  goto_set_num_threads(openmp_nthreads);
+    openmp_nthreads = blas_omp_number_max;
+  }
+
+  if (blas_cpu_number != openmp_nthreads) {
+    goto_set_num_threads(openmp_nthreads); // mutates `blas_cpu_number`
   }
 #endif
 
diff --git a/driver/others/blas_server_omp.c b/driver/others/blas_server_omp.c
index 38b48fc842..1f6e35e184 100644
--- a/driver/others/blas_server_omp.c
+++ b/driver/others/blas_server_omp.c
@@ -69,7 +69,8 @@
 
 int blas_server_avail = 0;
 int blas_omp_number_max = 0;
-int blas_omp_threads_local = 1;
+int blas_omp_threads_local = 1; // num threads to use when already inside omp_in_parallel()
+int blas_is_num_threads_set_explicitly = 0; // tracks whether the user called openblas_set_num_threads()
 
 extern int openblas_omp_adaptive_env(void);
 
@@ -122,7 +123,7 @@ void goto_set_num_threads(int num_threads) {
 
 }
 void openblas_set_num_threads(int num_threads) {
-
+	blas_is_num_threads_set_explicitly = 1;
 	goto_set_num_threads(num_threads);
 }