  This article is concerned with self-avoiding walks (SAW) on $\mathbb{Z}^{d}$
that are subject to a self-attraction. The attraction, which rewards instances
of adjacent parallel edges, introduces difficulties that are not present in
ordinary SAW. Ueltschi has shown how to overcome these difficulties for
sufficiently regular infinite-range step distributions and weak
self-attractions. This article considers the case of bounded step
distributions. For weak self-attractions we show that the connective constant
exists, and, in $d\geq 5$, carry out a lace expansion analysis to prove the
mean-field behaviour of the critical two-point function, hereby addressing a
problem posed by den Hollander.
