The technical aspects correlated with the observed enhancement of mass density and critical current density in the filaments of in situ MgB2 wires by means of the recently developed Cold High Pressure Densification (CHPD) are reviewed. The present analysis first summarizes the results obtained by means of a short sample prototype device with anvil lengths of 39 mm. Pressures well above 1 GPa were applied to short wires, causing Jc enhancements between a factor 1.5 and 2.3 at 4.2 K and 8 T. At 20 K, the enhancement is much stronger and reaches a factor 3 for binary and 5 for alloyed MgB2 wires. Based on these results, an automatic machine has been developed allowing a sequential press/release/advance operation. With this machine, which has been very recently installed at GAP in Geneva, in situ MgB2 wires of lengths up to 10 meters have so far been successfully densified, confirming the Jc enhancements obtained with the short sample device. Using an improved anvil geometry, the wall friction was reduced with respect to the short sample prototype device, thus yielding the same Jc enhancements, but at considerably lower applied pressures: now, Jc max was obtained at 0.85 GPa, in contrast to values between 1.3 and 1.5 GPa for the short sample device. After densifying at this pressure, the value of Jc = 1 × 104 A/cm2 at 4.2 K was obtained at 13.2 T over 1 m length, thus corresponding to an enhancement by a factor 2.2 with respect to the non pressed wire. The present results are promising in view of the application of CHPD to industrial wire lengths.