At CCS 2017, Espitau et al. described a side-channel attack against the rejection sampling step in BLISS signatures, and mentioned that the attack could be greatly improved and simplified for *uncompressed* BLISS signatures, as one could target the part of rejection sampling depending linearly on the secret key, as opposed to quadratically. In actual, compressed BLISS signatures, though, one only gets noisy linear relations on the secret, so key recovery amounts to solving a high-dimensional LWE-type problem. As a result, Espitau et al. dimissed this approach as infeasible. However, the LWE problem that arises in this way does not involve any modular reduction: it is defined over Z. With that motivation in mind, we study the hardness of LWE over the integers, and find that the problem (with polynomial size errors) can heuristically always be solved given sufficiently many samples. We also present provable results in that direction, and show that we can in fact mount the side-channel attack on BLISS, against 100% of secret keys (as opposed to ~7% in the CCS paper). This is joint work with J. Bootle (University College London).