OT: Best way to shrink size of video?

[joe at actionline.com]

What is the best (quickest and most efficient)
way to shrink the size of a video?

Someone sent a 11-second ".MOV" video that was
25-megabyte. I first tried to use mencoder to
convert it, but it did not work. So I used

https://cloudconvert.com/mov-to-mp4

to convert it from .mov to .mp4 and that cut the
size to about half.

Then I used www.videosmaller.com/ to convert it
to a smaller mp4.

Surely there must be a quicker, more efficient,
single-step way to get the best possible result
that still has "reasonably" good quality video.

-rw-r--r--25385488 Jul  9 17:40 IMG_0551.MOV
-rw-r--r-- 8525047 Jul  9 18:22 buff.mov
-rw-r--r--13196515 Jul  9 20:04 buffb4.mp4
-rw-r--r-- 7594494 Jul  9 20:07 buff.mp4

I uploaded the current 7.5-meg result here:

http://upquick.com/temp/buff.mp4