We discuss a new inflationary scenario which is realized within the extended supersymmetric Pati-Salam model which yields an acceptable b -quark mass for universal boundary conditions and \mu > 0 by modestly violating Yukawa unification and leads to new shifted , new smooth , or standard-smooth hybrid inflation . Inflation takes place along a “ semi-shifted ” classically flat direction on which the { U ( 1 ) _ { B - L } } gauge group remains unbroken . After the end of inflation , { U ( 1 ) _ { B - L } } breaks spontaneously and a network of local cosmic strings , which contribute a small amount to the curvature perturbation , is produced . We show that , in minimal supergravity , this “ semi-shifted ” inflationary scenario is compatible with a recent fit to data which uses field-theory simulations of a local string network . Taking into account the requirement of gauge unification , we find that , for spectral index n _ { s } = 1 , the predicted fractional contribution of strings to the temperature power spectrum at multipole \ell = 10 is f _ { 10 } \simeq 0.039 . Also , for f _ { 10 } = 0.10 , which is the best-fit value , we obtain n _ { s } \simeq 1.0254 . Spectral indices lower than about 0.98 are excluded and blue spectra are slightly favored . Magnetic monopoles are not formed at the end of semi-shifted hybrid inflation .