Kinship investigations such as paternity are currently solved using sets of (commercially available) highly polymorphic autosomal short tandem repeats (STRs), which lead to powerful likelihood ratios (LR). Still, some difficult cases arise whenever the kinship is much more remote or if the alternative hypotheses are not correctly formulated due to the lack of information (for e.g. there is an unknown relationship between the alleged and the true fathers). In these situations, beyond the routinely used marker set, laboratories usually enlarge the number and/or the type of markers analysed. Among these, autosomal indels and X-chromosome STRs have gained popularity. The aim of this study was to compare the results obtained after complementing an initial set of autosomal STRs with indels or with X-chromosome-specific STRs in simulated paternity cases where the alleged father is a close relative of the real one. Results show that in paternity cases where a low number of incompatibilities are observed, the best strategy is to increase the number of autosomal STRs under analysis. Nevertheless, if these are not available, our study globally shows that in father-daughter duos, a set of 12 X-STRs is more advantageous than 38 highly diverse autosomal biallelic markers. Additionally, the usefulness of X-STRs was also evaluated in cases where only a close relative of the alleged parent (father or mother) is available for testing. For those situations where these markers have the power to exclude, strong LR values are obtained. In the remaining cases, LRs are usually weak and sometimes the results are more likely under the wrong kinship hypothesis.