diff --git a/runtime/kubernetes/container.go b/runtime/kubernetes/container.go
index 4fa75d4..d4227ec 100644
--- a/runtime/kubernetes/container.go
+++ b/runtime/kubernetes/container.go
@@ -281,9 +281,15 @@ func (c *client) TailContainer(ctx context.Context, ctn *pipeline.Container) (io
 		//
 		// https://pkg.go.dev/k8s.io/api/core/v1?tab=doc#PodLogOptions
 		opts := &v1.PodLogOptions{
-			Container:  ctn.ID,
-			Follow:     true,
-			Previous:   false,
+			Container: ctn.ID,
+			Follow:    true,
+			// steps can exit quickly, and might be gone before
+			// log tailing has started, so we need to request
+			// logs for previously exited containers as well.
+			// Pods get deleted after job completion, and names for
+			// pod+container don't get reused. So, previous
+			// should only retrieve logs for the current build step.
+			Previous:   true,
 			Timestamps: false,
 		}