New STAR transverse spin results

New measurements of transverse single spin asymmetries at midrapidity of single hadrons and di-hadrons produced in jets are reported. They provide data on quark transversity in p+p collisions at RHIC. Pushing out to the Forward Meson Spectrometer (FMS) rapidities in future measurements will probe quark transversity at high x. Another transverse spin result from STAR is also reported: It is found that the π0 transverse single spin asymmetries at 2.5<η<4 extend to very high transverse momentum with no observed decrease.