The sensitivity of a low-noise superconducting transition edge sensor (TES) is determined by the thermal conductance of the support structure that connects the active elements of the device to the heat bath. Lownoise devices require conductances in the range 0.1 to 10 pW K −1 , and so have to rely on diffusive phonon scattering in long, narrow, amorphous SiN x legs. We show that it is possible to manufacture and operate TESs having short, ballistic low-dimensional legs (cross section 500 × 200 nm) that contain multi-element phononic interferometers and ring resonators. These legs transport heat in effectively just 5 elastic modes at the TES's operating temperature (< 150 mK), which is close to the quantised limit of 4. The phononic filters then reduce the thermal flux further by frequency-domain filtering. For example, a micromachined 3-element ring resonator reduced the flux to 19 % of a straight-legged ballistic device operating at the quantised limit, and 38 % of a straight-legged diffusive reference device. This work opens the way to manufacturing TESs where performance is determined entirely by filtered, few-mode, ballistic thermal transport in short, low-heat capacity legs, free from the artifacts of two level systems. arXiv:1805.09783v1 [cond-mat.mes-hall]