diff --git a/pkg/kgo/broker.go b/pkg/kgo/broker.go
index 5579dc83..3199eaef 100644
--- a/pkg/kgo/broker.go
+++ b/pkg/kgo/broker.go
@@ -8,6 +8,7 @@ import (
 	"fmt"
 	"io"
 	"math"
+	"math/rand"
 	"net"
 	"os"
 	"strconv"
@@ -948,7 +949,9 @@ func (cxn *brokerCxn) doSasl(authenticate bool) error {
 		if latencyMillis > minPessimismMillis {
 			minPessimismMillis = latencyMillis
 		}
-		maxPessimismMillis := float64(lifetimeMillis) * (0.05 - 0.03*cxn.b.cl.rng()) // 95 to 98% of lifetime (pessimism 2% to 5%)
+		var random float64
+		cxn.b.cl.rng(func(r *rand.Rand) { random = r.Float64() })
+		maxPessimismMillis := float64(lifetimeMillis) * (0.05 - 0.03*random) // 95 to 98% of lifetime (pessimism 2% to 5%)
 
 		// Our minimum lifetime is always 1s (or latency, if larger).
 		// When our max pessimism becomes more than min pessimism,
diff --git a/pkg/kgo/client.go b/pkg/kgo/client.go
index d1368f7e..0a02b01a 100644
--- a/pkg/kgo/client.go
+++ b/pkg/kgo/client.go
@@ -39,12 +39,12 @@ type Client struct {
 	ctx       context.Context
 	ctxCancel func()
 
-	rng func() float64
+	rng func(func(*rand.Rand))
 
 	brokersMu    sync.RWMutex
 	brokers      []*broker    // ordered by broker ID
 	seeds        atomic.Value // []*broker, seed brokers, also ordered by ID
-	anyBrokerIdx int32
+	anyBrokerOrd []int32      // shuffled brokers, for random ordering
 	anySeedIdx   int32
 	stopBrokers  bool // set to true on close to stop updateBrokers
 
@@ -462,13 +462,13 @@ func NewClient(opts ...Opt) (*Client, error) {
 		ctx:       ctx,
 		ctxCancel: cancel,
 
-		rng: func() func() float64 {
+		rng: func() func(func(*rand.Rand)) {
 			var mu sync.Mutex
 			rng := rand.New(rand.NewSource(time.Now().UnixNano()))
-			return func() float64 {
+			return func(fn func(*rand.Rand)) {
 				mu.Lock()
 				defer mu.Unlock()
-				return rng.Float64()
+				fn(rng)
 			}
 		}(),
 
@@ -733,9 +733,21 @@ func (c *connTimeouter) timeouts(req kmsg.Request) (r, w time.Duration) {
 	}
 }
 
+func (cl *Client) reinitAnyBrokerOrd() {
+	cl.anyBrokerOrd = append(cl.anyBrokerOrd[:0], make([]int32, len(cl.brokers))...)
+	for i := range cl.anyBrokerOrd {
+		cl.anyBrokerOrd[i] = int32(i)
+	}
+	cl.rng(func(r *rand.Rand) {
+		r.Shuffle(len(cl.anyBrokerOrd), func(i, j int) {
+			cl.anyBrokerOrd[i], cl.anyBrokerOrd[j] = cl.anyBrokerOrd[j], cl.anyBrokerOrd[i]
+		})
+	})
+}
+
 // broker returns a random broker from all brokers ever known.
 func (cl *Client) broker() *broker {
-	cl.brokersMu.Lock() // full lock needed for anyBrokerIdx below
+	cl.brokersMu.Lock()
 	defer cl.brokersMu.Unlock()
 
 	// Every time we loop through all discovered brokers, we issue one
@@ -743,23 +755,23 @@ func (cl *Client) broker() *broker {
 	// brokers are down, we will *eventually* loop through seeds and
 	// hopefully have a reachable seed.
 	var b *broker
-	if len(cl.brokers) > 0 && int(cl.anyBrokerIdx) < len(cl.brokers) {
-		cl.anyBrokerIdx %= int32(len(cl.brokers))
-		b = cl.brokers[cl.anyBrokerIdx]
-		cl.anyBrokerIdx++
-	} else {
-		seeds := cl.loadSeeds()
-		cl.anySeedIdx %= int32(len(seeds))
-		b = seeds[cl.anySeedIdx]
-		cl.anySeedIdx++
 
-		// If we have brokers, we ranged past discovered brokers.
-		// We now reset the anyBrokerIdx to begin ranging through
-		// discovered brokers again.
-		if len(cl.brokers) > 0 {
-			cl.anyBrokerIdx = 0
-		}
+	if len(cl.anyBrokerOrd) > 0 {
+		b = cl.brokers[cl.anyBrokerOrd[0]]
+		cl.anyBrokerOrd = cl.anyBrokerOrd[1:]
+		return b
 	}
+
+	seeds := cl.loadSeeds()
+	cl.anySeedIdx %= int32(len(seeds))
+	b = seeds[cl.anySeedIdx]
+	cl.anySeedIdx++
+
+	// If we have brokers, we ranged past discovered brokers.
+	// We now reset the anyBrokerOrd to begin ranging through
+	// discovered brokers again. If there are still no brokers,
+	// this reinit will do nothing and we will keep looping seeds.
+	cl.reinitAnyBrokerOrd()
 	return b
 }
 
@@ -946,6 +958,7 @@ func (cl *Client) updateBrokers(brokers []kmsg.MetadataResponseBroker) {
 	}
 
 	cl.brokers = newBrokers
+	cl.reinitAnyBrokerOrd()
 }
 
 // CloseAllowingRebalance allows rebalances, leaves any group, and closes all