Making the menu smaller

Yes, You Can do that, modify your css file. and use

line-height : desired value;

property to control the height of your menu. and there maybe other things like padding, margin etc. so modify their values also as you need.

Thanks aranwer104,

I’m not quite sure what you mean by “modify your css file.” though?

Am I to add a custom css-strip or am I to alter the already existing one?

There are options for this in the theme. Simply go to Customize > Menu and adjust there.

If your theme has builtin options for customizing menu as Vladff said then its very easy, you just have to adjust settings.. i hope it does.
but if there is no options for customizing menu height as you want, then yes you have add new values (height,width etc ) in you css file.