diff --git a/src/timer/SDL_timer.c b/src/timer/SDL_timer.c
index 2d6ad8b02..b47117e52 100644
--- a/src/timer/SDL_timer.c
+++ b/src/timer/SDL_timer.c
@@ -664,20 +664,71 @@ void SDL_DelayNS(Uint64 ns)
 void SDL_DelayPrecise(Uint64 ns)
 {
     Uint64 current_value = SDL_GetTicksNS();
-    Uint64 target_value = current_value + ns;
+    const Uint64 target_value = current_value + ns;
 
-    // Sleep for a short number of cycles
-    // We'll use 1 ms as a scheduling timeslice, it's a good value for modern operating systems
-    const int SCHEDULING_TIMESLICE_NS = 1 * SDL_NS_PER_MS;
-    while (current_value < target_value) {
-        Uint64 remaining_ns = (target_value - current_value);
-        if (remaining_ns > (SCHEDULING_TIMESLICE_NS + SDL_NS_PER_US)) {
-            // Sleep for a short time, less than the scheduling timeslice
-            SDL_SYS_DelayNS(SCHEDULING_TIMESLICE_NS - SDL_NS_PER_US);
-        } else {
-            // Spin for any remaining time
-            SDL_CPUPauseInstruction();
+    // Sleep for a short number of cycles when real sleeps are desired.
+    // We'll use 1 ms, it's the minimum guaranteed to produce real sleeps across
+    // all platforms.
+    const Uint64 SHORT_SLEEP_NS = 1 * SDL_NS_PER_MS;
+
+    // Try to sleep short of target_value. If for some crazy reason
+    // a particular platform sleeps for less than 1 ms when 1 ms was requested,
+    // that's fine, the code below can cope with that, but in practice no
+    // platforms behave that way.
+    Uint64 max_sleep_ns = SHORT_SLEEP_NS;
+    while (current_value + max_sleep_ns < target_value) {
+        // Sleep for a short time
+        SDL_SYS_DelayNS(SHORT_SLEEP_NS);
+
+        const Uint64 now = SDL_GetTicksNS();
+        const Uint64 next_sleep_ns = (now - current_value);
+        if (next_sleep_ns > max_sleep_ns) {
+            max_sleep_ns = next_sleep_ns;
         }
+        current_value = now;
+    }
+
+    // Do a shorter sleep of the remaining time here, less the max overshoot in
+    // the first loop. Due to maintaining max_sleep_ns as
+    // greater-than-or-equal-to-1 ms, we can always subtract off 1 ms to get
+    // the duration overshot beyond a 1 ms sleep request; if the system never
+    // overshot, great, it's zero duration. By choosing the max overshoot
+    // amount, we're likely to not overshoot here. If the sleep here ends up
+    // functioning like SDL_DelayNS(0) internally, that's fine, we just don't
+    // get to do a more-precise-than-1 ms-resolution sleep to undershoot by a
+    // small amount on the current system, but SDL_DelayNS(0) does at least
+    // introduce a small, yielding delay on many platforms, better than an
+    // unyielding busyloop.
+    //
+    // Note that we'll always do at least one sleep in this function, so the
+    // minimum resolution will be that of SDL_SYS_DelayNS()
+    if (current_value < target_value && (target_value - current_value) > (max_sleep_ns - SHORT_SLEEP_NS)) {
+        const Uint64 delay_ns = (target_value - current_value) - (max_sleep_ns - SHORT_SLEEP_NS);
+        SDL_SYS_DelayNS(delay_ns);
+        current_value = SDL_GetTicksNS();
+    }
+
+    // We've likely undershot target_value at this point by a pretty small
+    // amount, but maybe not. The footgun case if not handled here is where
+    // we've undershot by a large amount, like several ms, but still smaller
+    // than the amount max_sleep_ns overshot by; in such a situation, the above
+    // shorter-sleep block didn't do any delay, the if-block wasn't entered.
+    // Also, maybe the shorter-sleep undershot by several ms, so we still don't
+    // want to spin a lot then. In such a case, we accept the possibility of
+    // overshooting to not spin much, or if overshot here, not at all, keeping
+    // CPU/power usage down in any case. Due to scheduler sloppiness, it's
+    // entirely possible to end up undershooting/overshooting here by much less
+    // than 1 ms even if the current system's sleep function is only 1
+    // ms-resolution, as SDL_GetTicksNS() generally is better resolution than 1
+    // ms on the systems SDL supports.
+    while (current_value + SHORT_SLEEP_NS < target_value) {
+        SDL_SYS_DelayNS(SHORT_SLEEP_NS);
+        current_value = SDL_GetTicksNS();
+    }
+
+    // Spin for any remaining time
+    while (current_value < target_value) {
+        SDL_CPUPauseInstruction();
         current_value = SDL_GetTicksNS();
     }
 }
diff --git a/test/testtimer.c b/test/testtimer.c
index 9523cd0dd..bdf7e908f 100644
--- a/test/testtimer.c
+++ b/test/testtimer.c
@@ -213,7 +213,7 @@ int main(int argc, char *argv[])
         Uint64 total_overslept = 0;
 
         start = SDL_GetTicksNS();
-        SDL_DelayNS(1);
+        SDL_DelayPrecise(1);
         now = SDL_GetTicksNS();
         actual_delay = (now - start);
         SDL_Log("Minimum precise delay: %" SDL_PRIu64 " ns\n", actual_delay);
@@ -221,7 +221,7 @@ int main(int argc, char *argv[])
         SDL_Log("Timing 100 frames at 60 FPS\n");
         for (i = 0; i < 100; ++i) {
             start = SDL_GetTicksNS();
-            SDL_DelayNS(desired_delay);
+            SDL_DelayPrecise(desired_delay);
             now = SDL_GetTicksNS();
             actual_delay = (now - start);
             if (actual_delay > desired_delay) {