As a first aspect, the present invention is directed to a process for making a heat-shrinkable annular film, comprising: (A) extruding an annular extrudate downward from an annular die; (B) quenching the annular extrudate by applying a quenching liquid to the annular extrudate; (C) reheating the extrudate to an orientation temperature of from 130.degree. F. to 210.degree. F., resulting in a reheated annular extrudate; and (D) orienting the reheated annular extrudate while the reheated annular extrudate is in the solid state, the orientation being carried out with a total orientation factor of at least 2, so that the resulting oriented, heat-shrinkable film has a total free shrink at 185.degree. F. of at least 10 percent. The extrudate comprises at least one semi-crystalline polyamide selected from the group consisting of: (i) polyamide 6, (ii) polyamide 66, (iii) polyamide 6/66, and (iv) polyamide 6/12. The semi-crystalline polyamide makes up at least 5 volume percent of the annular extrudate. At least 50% of the quenching liquid cascades down the annular extrudate for a distance of at least 2 inches. The quenching liquid makes initial contact with the annular extrudate within 0.1 to 8 inches of the annular die.