The introduction of the test voltage function or k-factor in IEC 60060-1 Ed. 3 has been an important step to ensure reproducibility and traceability in high voltage tests techniques for lightning impulses with superposed oscillations and overshoots. The standard recommends computed fitting methods to extract a base curve from the oscillating recorded voltage curve and, applying the test voltage function, it is possible to calculate the impulse parameters. Testing external insulations with positive polarity lightning impulses at 50% breakdown voltage or lower level, the disruptive discharge usually arrives after ten microseconds. For these cases the test voltage function and procedures for calculating impulse parameters proposed by the standard may lead to divergent results. In this paper a new approach is proposed for fitting the base curve for metric air gaps based on the relevance of the leader propagation phase, highlighting the influence of the instantaneous voltage between the impulse crest and the time-tobreakdown. A comparison of three calculation methods for test curves with long timeto- breakdown is discussed and a new test voltage function obtained by measurements on a 1 m rod-plane air gap is proposed. Compared to the standard test voltage factor, this approach evidences a negligible influence of oscillations and the relevancy of the impulse tail voltage for testing external insulations with moderately distorted lightning impulses. Finally, a generalization of the voltage test function is proposed for several types of insulation considering mainly the average breakdown times.