In working further on a video project, I had to re-encode (reencode?) them to a lower bitrate for slower connections.

So far, this seems to work:

avconv -i in.mp4 -c:a copy -c:v libx264 -crf 28 -preset veryfast out.mp4

and then:

MP4Box -brand mp42 out.mp4

Further details here:

https://trac.ffmpeg.org/wiki/Encode/H.264