We demonstrate halving the record-low loss of interconnection between a nested antiresonant nodeless type hollow-core fiber (NANF) and standard single-mode fiber (SMF). The achieved interconnection loss of 0.15 dB is only 0.07 dB above the theoretically-expected minimum loss. We also optimized the interconnection in terms of unwanted cross-coupling into the higher-order modes of the NANF. We achieved cross-coupling as low as -35 dB into the LP[Formula: see text] mode (the lowest-loss higher-order mode and thus the most important to eliminate). With the help of simulations, we show that the measured LP[Formula: see text] mode coupling is most likely limited by the slightly imperfect symmetry of the manufactured NANF. The coupling cross-talk into the highly-lossy LP[Formula: see text] mode ([Formula: see text] dB/km in our fiber) was measured to be below -22 dB. Furthermore, we show experimentally that the anti-reflective coating applied to the interconnect interface reduces the insertion loss by 0.15 dB while simultaneously reducing the back-reflection below -40 dB over a 60 nm bandwidth. Finally, we also demonstrated an alternative mode-field adapter to adapt the mode-field size between SMF and NANF, based on thermally-expanded core fibers. This approach enabled us to achieve an interconnection loss of 0.21 dB and cross-coupling of -35 dB into the LP[Formula: see text] mode.