Quasi-longitudinal (QL) Anisimkin Jr.' modes discovered recently in quartz plates are found now in 2 other piezoelectric crystals, belonging to trigonal symmetry. In 128 degrees Y, X+90 degrees-LiNbO3, 2 different QL modes may propagate simultaneously for small plate thickness h/lambda = 0 to 0.06 (h is thickness, lambda is wavelength). The velocity of the 1st mode, v1, is close to the longitudinal bulk wave velocity vL. It is varied with h/lambda and piezoelectrically stiffened (maximum K(n)(2) = 39% at h/lambda = 0.08). The velocity of the 2nd QL mode, v2, is close to the shear-horizontal bulk wave velocity vQSH, not varied with h/lambda and not stiffened (K(n)(2) = 0). On the contrary, 210 degrees Y, X-Te crystal supports only one QL-mode, but it is unusually wide-ranging and low-dispersive: the mode exists for all h/lambda from 0 to 2.5 with velocity v(n) almost permanent and equal to vL in the whole range. This mode is piezoelectrically stiffened (maximum K(n)(2) = 2% at h/lambda = 0.13). The variety of the Anisimkin Jr.' modes in different crystals makes them attractive for liquid sensors, where the amount of suitable waves is very restricted.