Mine is much like the one from Harbor Freight minus the handle.  I don't know what the minimum height is, but it was low enough to get under that Honda Civic.  I have it somewhere in my automotive junk pile but haven't used it in years.
I first found out about and fell in love with Harbor Freight when they sent me a catalog out of the clear blue years ago.  While purusing the catalog, I found a 2 1/2 ton capacity floor jack that lifts 31 5/8", their model no. 42820-5VGA.  Being on the heavy side, the clearance was a god send for me.  I bought (4) 6 ton jack stands because they were capable of being raised to 29" to hold my cars way up there when I have to work underneath them.
Bountyhunter