Since в смисъла на "щом".

Since you want it that much, I will buy you your own car.
Since there was nobody left at the studio, he packed his stuff and left.

Yet и still в смисъла на "все пак" / "въпреки това"

The marines' line of work is one of great hazard, yet most of the soldiers do not doubt their decision, to serve their country.

The exam will be rather easy compared to ones from previous terms. Still, many students are overly stressed because of the upcoming event.