We report results of a new analysis of a deep 95 \mu m imaging survey with the photo-polarimeter ISOPHOT on board the Infrared Space Observatory , over a 40 ^ { \prime } \times 40 ^ { \prime } area within the Lockman Hole . To this end we exploit a newly developed parametric algorithm able to identify and clean spurious signals induced by cosmic-rays impacts and by transient effects and non-linearities in the detectors . These results provide us with the currently deepest – to our knowledge – far-IR image of the extragalactic sky . Within the survey area we detect thirty-six sources with S/N > 3 ( corresponding to a flux of 16 mJy ) , making up a complete flux-limited sample for S _ { 95 \mu m } \geq 100 mJy . Reliable sources are detected , with decreasing but well-controlled completeness , down to S _ { 95 \mu m } \simeq 20 mJy . The source extraction process and the completeness , the photometric and astrometric accuracies of this catalogue have been tested by us with extensive simulations accounting for all the details of the procedure . We estimate source counts down to a flux of \sim 30 mJy , at which limit we evaluate that from 10 % to 20 % of the cosmic IR background has been resolved into sources ( contributing to the CIRB intensity \simeq 2.0 10 ^ { -9 } W / m ^ { 2 } / sr ) . The 95 \mu m galaxy counts reveal a steep slope at S _ { 95 \mu m } \leq 100 mJy ( \alpha \simeq 1.6 ) , in excess of that expected for a non-evolving source population . The shape of these counts agrees with those determined by ISO at 15 and 175 \mu m , and starts setting strong constraints on the evolution models for the far-IR galaxy populations .