This paper deals with the problem of determining small-bands enclosing a given set of points on the sphere. The small-band is a spherical region, whose boundary is composed of two circles, and which does not contain any great circle. It is a kind of domains that is derived from formalizing the local accessibility problems for 3-axis NC machining into sperical containment problems so as to avoid the grouping. It also can be generated in 4- and 5-axis machine. When a set of points U and the size of a great-band are given, the methods for computing a feasible band and all feasible bands enclosing U in O(n) and O(n log n) time have been suggested, respectively. The methods can be applied into the cases of small bands since the solution region may contain holes. In this paper, we concentrate on the method for determining the smallest small-band enclosing U and suggest an O(n long n) time algorithm, where n is the number of points on the sphere.