The parameter space for A -term inflation is explored with W = \lambda _ { p } \phi ^ { p } / pM _ { P } ^ { p - 3 } .
With p = 6 and \lambda _ { p } \sim 1 , the observed spectrum and spectral tilt can be obtained with soft mass of order 10 ^ { 2 } \mbox { GeV } but not with a much higher mass .
The case p = 3 requires \lambda _ { p } \sim 10 ^ { -9 } to 10 ^ { -12 } .
The ratio m / A requires fine-tuning , which may be justified on environmental grounds .
An extension of the MSSM to include non-renormalizable terms and/or Dirac neutrino masses might support either A -term inflation or modular inflation .