Comparisons of two optical clocks based on the E2 and E3 optical clock transitions in ¹⁷¹Yb⁺ at PTB have been analysed for potential violations of local position invariance. The limits for fractional temporal variations of the fine structure constant and the proton-to-electron mass ratio have been improved by factors of about 20 and 2 respectively. Limits for a potential coupling of both constants to gravity have also been improved. The results were published in Physical Review Letters on 6th January.