diff --git a/benchmarks/bench-objsort.hpp b/benchmarks/bench-objsort.hpp
index 4f5719a..b61364a 100644
--- a/benchmarks/bench-objsort.hpp
+++ b/benchmarks/bench-objsort.hpp
@@ -13,9 +13,9 @@ struct Point3D {
     static constexpr std::string_view name {val};
     Point3D()
     {
-        x = (T)rand() / RAND_MAX;
-        y = (T)rand() / RAND_MAX;
-        z = (T)rand() / RAND_MAX;
+        x = (T)rand() / (T)RAND_MAX;
+        y = (T)rand() / (T)RAND_MAX;
+        z = (T)rand() / (T)RAND_MAX;
     }
     T distance()
     {
diff --git a/src/xss-common-argsort.h b/src/xss-common-argsort.h
index eb46bbe..70eec0b 100644
--- a/src/xss-common-argsort.h
+++ b/src/xss-common-argsort.h
@@ -472,7 +472,8 @@ X86_SIMD_SORT_INLINE void argsort_(type_t *arr,
                                    arrsize_t *arg,
                                    arrsize_t left,
                                    arrsize_t right,
-                                   arrsize_t max_iters)
+                                   arrsize_t max_iters,
+                                   arrsize_t task_threshold)
 {
     /*
      * Resort to std::sort if quicksort isnt making any progress
@@ -494,11 +495,57 @@ X86_SIMD_SORT_INLINE void argsort_(type_t *arr,
     type_t biggest = vtype::type_min();
     arrsize_t pivot_index = argpartition_unrolled<vtype, argtype, 4>(
             arr, arg, left, right + 1, pivot, &smallest, &biggest);
+#ifdef XSS_COMPILE_OPENMP
+    if (pivot != smallest) {
+        bool parallel_left = (pivot_index - left) > task_threshold;
+        if (parallel_left) {
+#pragma omp task
+            argsort_<vtype, argtype>(arr,
+                                     arg,
+                                     left,
+                                     pivot_index - 1,
+                                     max_iters - 1,
+                                     task_threshold);
+        }
+        else {
+            argsort_<vtype, argtype>(arr,
+                                     arg,
+                                     left,
+                                     pivot_index - 1,
+                                     max_iters - 1,
+                                     task_threshold);
+        }
+    }
+    if (pivot != biggest) {
+        bool parallel_right = (right - pivot_index) > task_threshold;
+
+        if (parallel_right) {
+#pragma omp task
+            argsort_<vtype, argtype>(arr,
+                                     arg,
+                                     pivot_index,
+                                     right,
+                                     max_iters - 1,
+                                     task_threshold);
+        }
+        else {
+            argsort_<vtype, argtype>(arr,
+                                     arg,
+                                     pivot_index,
+                                     right,
+                                     max_iters - 1,
+                                     task_threshold);
+        }
+    }
+#else
+    UNUSED(task_threshold);
     if (pivot != smallest)
         argsort_<vtype, argtype>(
-                arr, arg, left, pivot_index - 1, max_iters - 1);
+                arr, arg, left, pivot_index - 1, max_iters - 1, 0);
     if (pivot != biggest)
-        argsort_<vtype, argtype>(arr, arg, pivot_index, right, max_iters - 1);
+        argsort_<vtype, argtype>(
+                arr, arg, pivot_index, right, max_iters - 1, 0);
+#endif
 }
 
 template <typename vtype, typename argtype, typename type_t>
@@ -570,8 +617,43 @@ X86_SIMD_SORT_INLINE void xss_argsort(T *arr,
             }
         }
         UNUSED(hasnan);
+
+#ifdef XSS_COMPILE_OPENMP
+
+        bool use_parallel = arrsize > 10000;
+
+        if (use_parallel) {
+            // This thread limit was determined experimentally; it may be better for it to be the number of physical cores on the system
+            constexpr int thread_limit = 8;
+            int thread_count = std::min(thread_limit, omp_get_max_threads());
+            arrsize_t task_threshold
+                    = std::max((arrsize_t)10000, arrsize / 100);
+
+            // We use omp parallel and then omp single to setup the threads that will run the omp task calls in qsort_
+            // The omp single prevents multiple threads from running the initial qsort_ simultaneously and causing problems
+            // Note that we do not use the if(...) clause built into OpenMP, because it causes a performance regression for small arrays
+#pragma omp parallel num_threads(thread_count)
+#pragma omp single
+            argsort_<vectype, argtype>(arr,
+                                       arg,
+                                       0,
+                                       arrsize - 1,
+                                       2 * (arrsize_t)log2(arrsize),
+                                       task_threshold);
+#pragma omp taskwait
+        }
+        else {
+            argsort_<vectype, argtype>(arr,
+                                       arg,
+                                       0,
+                                       arrsize - 1,
+                                       2 * (arrsize_t)log2(arrsize),
+                                       std::numeric_limits<arrsize_t>::max());
+        }
+#else
         argsort_<vectype, argtype>(
-                arr, arg, 0, arrsize - 1, 2 * (arrsize_t)log2(arrsize));
+                arr, arg, 0, arrsize - 1, 2 * (arrsize_t)log2(arrsize), 0);
+#endif
 
         if (descending) { std::reverse(arg, arg + arrsize); }
     }
diff --git a/src/xss-common-keyvaluesort.hpp b/src/xss-common-keyvaluesort.hpp
index a607b62..1a15de7 100644
--- a/src/xss-common-keyvaluesort.hpp
+++ b/src/xss-common-keyvaluesort.hpp
@@ -627,6 +627,7 @@ X86_SIMD_SORT_INLINE void xss_qsort_kv(
                                       index_last_elem,
                                       maxiters,
                                       task_threshold);
+#pragma omp taskwait
         }
         else {
             kvsort_<keytype, valtype>(keys,
@@ -636,7 +637,6 @@ X86_SIMD_SORT_INLINE void xss_qsort_kv(
                                       maxiters,
                                       std::numeric_limits<arrsize_t>::max());
         }
-#pragma omp taskwait
 #else
         kvsort_<keytype, valtype>(
                 keys, indexes, 0, index_last_elem, maxiters, 0);
diff --git a/src/xss-common-qsort.h b/src/xss-common-qsort.h
index 5108e38..e3bf019 100644
--- a/src/xss-common-qsort.h
+++ b/src/xss-common-qsort.h
@@ -682,6 +682,7 @@ X86_SIMD_SORT_INLINE void xss_qsort(T *arr, arrsize_t arrsize, bool hasnan)
                                          arrsize - 1,
                                          2 * (arrsize_t)log2(arrsize),
                                          task_threshold);
+#pragma omp taskwait
         }
         else {
             qsort_<vtype, comparator, T>(arr,
@@ -690,7 +691,6 @@ X86_SIMD_SORT_INLINE void xss_qsort(T *arr, arrsize_t arrsize, bool hasnan)
                                          2 * (arrsize_t)log2(arrsize),
                                          std::numeric_limits<arrsize_t>::max());
         }
-#pragma omp taskwait
 #else
         qsort_<vtype, comparator, T>(
                 arr, 0, arrsize - 1, 2 * (arrsize_t)log2(arrsize), 0);
diff --git a/tests/test-qsort.cpp b/tests/test-qsort.cpp
index 3083f72..869ecea 100644
--- a/tests/test-qsort.cpp
+++ b/tests/test-qsort.cpp
@@ -89,7 +89,7 @@ TYPED_TEST_P(simdsort, test_argsort_ascending)
 {
     for (auto type : this->arrtype) {
         bool hasnan = is_nan_test(type);
-        for (auto size : this->arrsize) {
+        for (auto size : this->arrsize_long) {
             std::vector<TypeParam> arr = get_array<TypeParam>(type, size);
             std::vector<TypeParam> sortedarr = arr;
 
@@ -110,7 +110,7 @@ TYPED_TEST_P(simdsort, test_argsort_descending)
 {
     for (auto type : this->arrtype) {
         bool hasnan = is_nan_test(type);
-        for (auto size : this->arrsize) {
+        for (auto size : this->arrsize_long) {
             std::vector<TypeParam> arr = get_array<TypeParam>(type, size);
             std::vector<TypeParam> sortedarr = arr;