diff --git a/libtransmission/bandwidth.cc b/libtransmission/bandwidth.cc
index ea0bfee41..92d89748f 100644
--- a/libtransmission/bandwidth.cc
+++ b/libtransmission/bandwidth.cc
@@ -4,7 +4,8 @@
 // License text can be found in the licenses/ folder.
 
 #include <algorithm>
-#include <utility> // std::swap()
+#include <random> // for std::mt19937
+#include <utility> // for std::swap()
 #include <vector>
 
 #include <fmt/core.h>
@@ -12,7 +13,6 @@
 #include "transmission.h"
 
 #include "bandwidth.h"
-#include "crypto-utils.h" // tr_rand_int()
 #include "log.h"
 #include "peer-io.h"
 #include "tr-assert.h"
@@ -166,31 +166,38 @@ void tr_bandwidth::allocateBandwidth(
 
 void tr_bandwidth::phaseOne(std::vector<tr_peerIo*>& peer_array, tr_direction dir)
 {
-    /* First phase of IO. Tries to distribute bandwidth fairly to keep faster
-     * peers from starving the others. Loop through the peers, giving each a
-     * small chunk of bandwidth. Keep looping until we run out of bandwidth
-     * and/or peers that can use it */
+    // First phase of IO. Tries to distribute bandwidth fairly to keep faster
+    // peers from starving the others.
     tr_logAddTrace(fmt::format("{} peers to go round-robin for {}", peer_array.size(), dir == TR_UP ? "upload" : "download"));
 
-    auto n = peer_array.size();
-    while (n > 0)
+    // Shuffle the peers so they all have equal chance to be first in line.
+    thread_local auto random_engine = std::mt19937{ std::random_device{}() };
+    std::shuffle(std::begin(peer_array), std::end(peer_array), random_engine);
+
+    // Give each peer `Increment` bandwidth bytes to use. Repeat this
+    // process until we run out of bandwidth and/or peers that can use it.
+    for (size_t n_unfinished = std::size(peer_array); n_unfinished > 0U;)
     {
-        auto const i = tr_rand_int(n); /* pick a peer at random */
-
-        // value of 3000 bytes chosen so that when using µTP we'll send a full-size
-        // frame right away and leave enough buffered data for the next frame to go
-        // out in a timely manner.
-        static auto constexpr Increment = size_t{ 3000 };
-
-        auto const bytes_used = peer_array[i]->flush(dir, Increment);
-
-        tr_logAddTrace(fmt::format("peer #{} of {} used {} bytes in this pass", i, n, bytes_used));
-
-        if (bytes_used != Increment)
+        for (size_t i = 0; i < n_unfinished;)
         {
-            // peer is done writing for now; move it to the end of the list
-            std::swap(peer_array[i], peer_array[n - 1]);
-            --n;
+            // Value of 3000 bytes chosen so that when using µTP we'll send a full-size
+            // frame right away and leave enough buffered data for the next frame to go
+            // out in a timely manner.
+            static auto constexpr Increment = size_t{ 3000 };
+
+            auto const bytes_used = peer_array[i]->flush(dir, Increment);
+            tr_logAddTrace(fmt::format("peer #{} of {} used {} bytes in this pass", i, n_unfinished, bytes_used));
+
+            if (bytes_used != Increment)
+            {
+                // peer is done writing for now; move it to the end of the list
+                std::swap(peer_array[i], peer_array[n_unfinished - 1]);
+                --n_unfinished;
+            }
+            else
+            {
+                ++i;
+            }
         }
     }
 }