The Swap-Insert Correction distance from a string S of length n to another string L of length in m >= n on the alphabet [1..sigma] is the minimum number of insertions, and swaps of pairs of adjacent symbols, converting S into L. Contrarily to other correction distances, computing it is NP-Hard in the size sigma of the alphabet. We describe an algorithm computing this distance in time within O(sigma(2) nmg(sigma-1)), where for each alpha is an element of [1..sigma] there are n(alpha) occurrences of alpha in S, m(alpha) occurrences of alpha in L, and where g = max(alpha)(is an element of)([1..sigma]) min{n(alpha),m(alpha) - n(alpha)} is a new parameter of the analysis, measuring one aspect of the difficulty of the instance. The difficulty g is bounded by above by various terms, such as the length n of the shortest string S, and by the maximum number of occurrences of a single character in S (max(alpha)(is an element of)([1..sigma]) n(alpha)) This result illustrates how, in many cases, the correction distance between two strings can be easier to compute than in the worst case scenario.