Relaxing the assumptions about the experimental setup in Quantum Key Distribution protocols lays the foundation for Device Independent Quantum Key Distribution (DIQKD). In the finite key regime of DIQKD, the protocols employ the use of only the CHSH inequality, so far. A natural question therefore arises whether are there other Bell inequalities that help achieve better results (in terms of higher rates, greater noise tolerance and lower number of minimum rounds required for positive rates) than those achieved using CHSH inequality? For the inequalities considered, we find that CHSH fares the best on account of noise tolerance. However, considering the other two parameters of interest we present two bipartite Bell-inequalities with three outcomes per party that perform better than CHSH for a certain range of noise involved.