Flutes are flow-parallel till ridges that form subglacially and are conspicuous geomorphic indicators of slip at glacier beds. Flutes commonly have a boulder at their head, lodged in the former till bed of the glacier. In the leading model of flute genesis, weak till of the bed flows into a water-filled cavity where ice separates from the lee surface of the boulder. This cavity is displaced downstream as it progressively fills with till and the flute lengthens. To test this hypothesis, we studied in detail a parallel-sided flute, 250 m long, and a tapered flute, 5 m long, at the surge-type glacier, Múlajökull, in Iceland. More than 900 measurements of till magnetic susceptibility anisotropy, calibrated experimentally, show that spatially averaged till flow converged toward flute long axes, consistent with the cavity-fill hypothesis, and that till shear strains were small (<7.6). Till density patterns indicate that decreasing water pressure in cavities, decreasing slip velocity, and associated increases in ice pressure on the distal ends of the flutes consolidated and strengthened till—an effect far more prominent in the long flute. This till strengthening resolves the fundamental mechanical problem that undermines the cavity-fill hypothesis: how a leeward cavity can be sustained well beyond the pressure shadow in ice created by a boulder. Also resolved is how convergent fabrics in flutes are preserved, despite significant slip of ice across them. These results provide the first evidence that flute elongation beneath wet-based glaciers may require fluctuating water pressure and slip velocity.