Small cross and small upside down cross symbols

I need a cross symbol, similar to \dagger, but optimally less fancy, smaller (not as long vertical line below the crossing) and without having to load a special symbol package (besides amsmath). The letter "t" without the bottom curve would do.

I also need the cross upside down (for mathematical and not religious reasons...). If I use sth. like \newcommand{\rotatedCross}{\ensuremath{\rotatebox[origin=c]{180}{\ensuremath{\dagger}}}}%, I get error messages if I use \rotatedCross inside other complex commands (use of \complexCommand doesn't match its definition). So the same cross upside down as own symbol (or a simpler solution than rotatebox) would be perfect.