The tendencies to phase-separation and stripe formation of the t-J model on
planes and four-leg ladders have been here reexamined including hole hoppi
ng terms t',t " beyond nearest-neighbor sites. The motivation for this stud
y is the growing evidence that such terms are needed for a quantitative des
cription of the cuprates. Using a variety of computational techniques it is
concluded that the stripe tendencies considerably weaken when experimental
ly realistic t'<0, t ">0 for hole-doped cuprates are considered. However, a
small t'>0 actually enhances the stripe formation. [S0163-1829(99)51218-6]
.