I present the first 1.3-mm observations of a complete sample of 10 X-r
ay-selected BL Lacertae objects (XBLs), together with complementary me
asurements of a complete sample of nine radio-selected BL Lacs (RBLs).
Three XBLs have firm detections and one has a marginally significant
detection. None of the XBLs has a radio spectrum rising steeply into t
he millimetre region, and the radio-millimetre spectral indices of the
XBLs detected are within the range found for the RBLs. However, the o
verall millimetre-X-ray spectra of the XBLs are much flatter than for
any RBL.