Efficient searching for specific subsequences in a set of longer sequences is an important component of many bioinformatics algorithms. Generalised suffix trees and suffix arrays allow searches for a pattern of length n in time proportional to n independent of the length of the sequences, and are thus attractive for a variety of applications. Here, we present an algorithm termed the generalised k-Truncated Suffix Tree (kTST), that represents an adaption of Ukkonen's linear-time suffix tree construction algorithm. The kTST algorithm creates a k-deep tree in linear time that allows rapid searches for short patterns of length of up to k characters. The kTST can offer advantages in computational time and memory usage for searches for short sequences in DNA or protein sequences compared to other suffix-based algorithms.