In this paper, we continue the theme of analytical and numerical treatment of Jungck-type iterative schemes. In particular, we focus on a special case of Jungck-Khan iterative scheme introduced by Khan et al. [Analytical and numerical treatment of Jungck-type iterative schemes, Appl. Math. Comput. 231 (2014) 521-535] to get an insight in the strong convergence and data dependence results obtained therein. Our investigations show that this special case under different control conditions on parametric sequences provides higher convergence rate and better data dependence estimates as compared to the Jungck-Khan iterative scheme itself.