diff --git a/build/Dockerfile b/build/Dockerfile
index 74904563..46b584bc 100644
--- a/build/Dockerfile
+++ b/build/Dockerfile
@@ -1,6 +1,12 @@
 FROM ubuntu
-# After installing the prerequisite we clear out sources.list so that
-# 'apt-get update' doesn't do anything.
+
+# When doing a build in a container, "apt-get update" happens twice,
+# which can be a very significant overhead for incremental builds.
+# And it's unnecessary, because if any of the prerequisites do change,
+# the right thing to do is to rebuild the container image.  Rather
+# than suppressing the "apt-get update" commands explicitly, we clear
+# out sources.list so that 'apt-get update' doesn't do anything.
+
 RUN sh -c 'apt-get -y update && apt-get -y install --no-install-recommends build-essential git ca-certificates golang docker.io mercurial libpcap-dev curl make pkg-config gcc bison flex && echo >/etc/apt/sources.list'
 COPY build.sh /
 ENTRYPOINT ["sh", "/build.sh"]
diff --git a/tools/build.sh b/tools/build.sh
index 2bfd2e0f..87528a09 100644
--- a/tools/build.sh
+++ b/tools/build.sh
@@ -1,4 +1,6 @@
 #!/bin/sh
+
+# Show the progress of this script, in case it fails.
 set -x -e
 
 sudo apt-get -y update