Investigations were made into the effect of small additions of Ni, Mo, Sn, as well as larger additions of Al on the magnetostriction of single crystal Fe100-xGax alloys (xcongruent to13). The Fe-Ga and Fe-Al systems are seemingly unique among the Fe-based alloys in having very large magnetostrictions in spite of Ga and Al being nonmagnetic. In this paper, we show how additions of Ni, Mo, Sn, and Al affect lambda(100) and lambda(111) of the binary Fe-Ga alloys. We substituted small amounts of Ni into a binary Fe-Ga alloy in an attempt to reduce the magnitude of the negative lambda(111), as Ni does in Fe, in order to improve the magnetostriction of polycrystals. The measured lambda(111)'s were reduced to a very small value, similar to3 ppm, but lambda(100) fell dramatically to +67 ppm for Fe86Ga11Ni3. Mo was substituted for Ga to determine the effect of a partially filled 4d shell on the magnetostriction. Here \lambda(111)\ is affected the most, increasing to a value greater than all known alpha-Fe-based alloys (lambda(111)=-22 ppm for Fe85Ga10.2Mo4.8). We find that the addition of Sn, with its very large atomic radius, makes only small changes in both lambda(100) and lambda(111). For Fe86.1Ga12.4Sn1.5 at room temperature, lambda(100)=+161 ppm and for Fe86.7Ga12.0Sn1.3, lambda(111)=-15 ppm. The decrease of lambda(100) in Fe-87(GayAl1-y)(13) was approximately linear, going from 67 ppm at y=0 to 154 ppm at y=1. (C) 2002 American Institute of Physics.