jb90

I use GHS pressurewounds for the higher tension and to lose the finger noise associated with rounds.  Less bright than rounds but brighter than regular flats.  Some used ones for sale right now (not by me).  You could do worse.  

Or you could try the new set of GHS Brite Flats that I have sale, though I haven't tried them so I couldn't say what the tension or tone is like from a personal perspective.

I also felt the TI flats were too loose for my tastes.  My go-to is now the La Bella 760FL which to me feels more like a roundwound, tension-wise.  For even more tension, check out the Rotosound Jazz 77s.  These for me are actually too tight for standard tuning, however I have them on a bass that's drop tuned half a step and they are perfect.  I'd be interested to try D'Addario Chromes too which seem to be highly rated among flats players.

Give Fender flats a go - probably the cheapest flatwound on the market and sound decent. Fairly high tension, which suited me.