In this paper we describe a new approach for millimeter Very Long Baseline Interferometry (mm-VLBI) calibration that provides bona-fide astrometric alignment of the millimeter-wavelength images from a single source, for the measurement of frequency-dependent effects, such as "core-shifts" near the black hole of active galactic nucleus jets. We achieve our astrometric alignment by solving first for the ionospheric (dispersive) contributions using wide-band centimeter-wavelength observations. Second, we solve for the tropospheric (non-dispersive) contributions by using fast frequency-switching at the target millimeter-wavelengths. These solutions can be scaled and transferred from low frequency to the high frequency. To complete the calibration chain an additional step is required to remove a residual constant phase offset on each antenna. The result is an astrometric calibration and the measurement of the core-shift between 22 and 43 GHz for the jet in BL Lacertae to be -8 ±5, 20 ±6 μas, in R.A. and decl., respectively. By comparison to conventional phase referencing at centimeter-wavelengths we are able to show that this core shift at millimeter-wavelengths is significantly less than what would be predicted by extrapolating the low-frequency result, which closely followed the predictions of the Blandford & Kö nigl conical jet model. As such it would be the first demonstration for the association of the VLBI core with a recollimation shock, normally hidden at low frequencies due to the optical depth, which could be responsible for the γ-ray production in blazar jets.