diff --git a/relay/limiter/blob_rate_limiter.go b/relay/limiter/blob_rate_limiter.go
index 07351834b0..e1c9173e91 100644
--- a/relay/limiter/blob_rate_limiter.go
+++ b/relay/limiter/blob_rate_limiter.go
@@ -112,8 +112,13 @@ func (l *BlobRateLimiter) RequestGetBlobBandwidth(now time.Time, bytes uint32) e
 		if l.relayMetrics != nil {
 			l.relayMetrics.ReportBlobRateLimited("global bandwidth")
 		}
-		return fmt.Errorf("global rate limit %dMib/s exceeded for getBlob bandwidth, try again later",
-			int(l.config.MaxGetBlobBytesPerSecond/1024/1024))
+
+		rateLimit := l.config.MaxGetBlobBytesPerSecond / 1024 / 1024
+		burstiness := l.config.GetBlobBytesBurstiness / 1024 / 1024
+
+		return fmt.Errorf(
+			"global rate limit %0.1fMiB/s (burstiness %dMiB) exceeded for getBlob bandwidth, try again later",
+			rateLimit, burstiness)
 	}
 	return nil
 }
diff --git a/relay/limiter/chunk_rate_limiter.go b/relay/limiter/chunk_rate_limiter.go
index e529d8b2c5..5632926c2a 100644
--- a/relay/limiter/chunk_rate_limiter.go
+++ b/relay/limiter/chunk_rate_limiter.go
@@ -162,8 +162,13 @@ func (l *ChunkRateLimiter) RequestGetChunkBandwidth(now time.Time, requesterID s
 		if l.relayMetrics != nil {
 			l.relayMetrics.ReportChunkRateLimited("global bandwidth")
 		}
-		return fmt.Errorf("global rate limit %dMiB exceeded for GetChunk bandwidth, try again later",
-			int(l.config.MaxGetChunkBytesPerSecond/1024/1024))
+
+		rateLimit := l.config.MaxGetChunkBytesPerSecond / 1024 / 1024
+		burstiness := l.config.GetChunkBytesBurstiness / 1024 / 1024
+
+		return fmt.Errorf(
+			"global rate limit %0.1fMiB (burstiness %dMIB) exceeded for GetChunk bandwidth, try again later",
+			rateLimit, burstiness)
 	}
 
 	limiter, ok := l.perClientBandwidthLimiter[requesterID]
@@ -176,8 +181,13 @@ func (l *ChunkRateLimiter) RequestGetChunkBandwidth(now time.Time, requesterID s
 		if l.relayMetrics != nil {
 			l.relayMetrics.ReportChunkRateLimited("client bandwidth")
 		}
-		return fmt.Errorf("client rate limit %dMiB exceeded for GetChunk bandwidth, try again later",
-			int(l.config.MaxGetChunkBytesPerSecondClient/1024/1024))
+
+		rateLimit := l.config.MaxGetChunkBytesPerSecondClient / 1024 / 1024
+		burstiness := l.config.GetChunkBytesBurstinessClient / 1024 / 1024
+
+		return fmt.Errorf(
+			"client rate limit %0.1fMiB (bustiness %dMiB) exceeded for GetChunk bandwidth, try again later",
+			rateLimit, burstiness)
 	}
 
 	return nil
diff --git a/relay/server.go b/relay/server.go
index 5fbce7c43b..a489b2768e 100644
--- a/relay/server.go
+++ b/relay/server.go
@@ -336,7 +336,7 @@ func (s *Server) GetChunks(ctx context.Context, request *pb.GetChunksRequest) (*
 		if strings.Contains(err.Error(), "internal error") {
 			return nil, api.NewErrorInternal(err.Error())
 		}
-		return nil, api.NewErrorResourceExhausted(fmt.Sprintf("bandwidth limit exceeded: %v", err))
+		return nil, buildInsufficientGetChunksBandwidthError(request, mMap, err)
 	}
 	s.metrics.ReportChunkDataSize(requiredBandwidth)
 
@@ -469,6 +469,37 @@ func computeChunkRequestRequiredBandwidth(request *pb.GetChunksRequest, mMap met
 	return requiredBandwidth, nil
 }
 
+// buildInsufficientBandwidthError builds an informative error message for when there is insufficient
+// bandwidth to serve a GetChunks() request.
+func buildInsufficientGetChunksBandwidthError(
+	request *pb.GetChunksRequest,
+	mMap metadataMap,
+	originalError error) error {
+
+	sb := strings.Builder{}
+	sb.WriteString("unable to serve chunks ")
+	for i, chunkRequest := range request.ChunkRequests {
+		var prefix string
+		var chunkCount int
+
+		if chunkRequest.GetByIndex() != nil {
+			prefix = "i"
+			chunkCount = len(chunkRequest.GetByIndex().ChunkIndices)
+		} else {
+			prefix = "r"
+			chunkCount = int(chunkRequest.GetByRange().EndIndex - chunkRequest.GetByRange().StartIndex)
+		}
+		chunkSize := int(mMap[v2.BlobKey(chunkRequest.GetByRange().GetBlobKey())].chunkSizeBytes)
+
+		sb.WriteString(fmt.Sprintf("%s(%d*%dbytes)", prefix, chunkCount, chunkSize))
+		if i < len(request.ChunkRequests)-1 {
+			sb.WriteString(", ")
+		}
+	}
+
+	return api.NewErrorResourceExhausted(fmt.Sprintf("%s: %v", sb.String(), originalError))
+}
+
 // Start starts the server listening for requests. This method will block until the server is stopped.
 func (s *Server) Start(ctx context.Context) error {
 	s.metrics.Start()