>
> For completeness, you may consider also handling the case where 
> completions-header-format is an empty string, which is another not too 
> unreasonable way to disable the header. minibuffer-next-completion still 
> skips the first candidate for that case.
>

Thanks for your feedback!  Indeed, that's another bug, which makes a fix 
elsewhere in the code even less likely.  It is fixed in the attached 
patch.  Can you try it?

Eli, do you have objections to that patch?