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The Maunder Minimum was a period with significantly reduced solar activity between 1645 and 1715, approximately. The transition between the low solar activity in the Maunder Minimum and the subsequent "normal" regime of solar activity was gradual. However, there are discrepancies in the solar activity level from sunspot number indices and solar activity proxies in that period. Among the contemporaneous observers, Johann L. Rost and Sebastian Alischer were two key sunspot observers to understand the solar activity in this transition just after the Maunder Minimum. We have revised all their sunspot records, counting the number of groups and individual sunspots to derive reliable data for the solar activity level for the period 1716–1726. We found significant misinterpretations of the sunspot group counting assigned to these astronomers in the existing group number databases. Our new group sunspot counting significantly reduces the number of groups for Rost and Alischer's observations compared to entries in existing databases. Furthermore, our sunspot number estimates (obtained from the active day fraction methodology) of the maximum amplitude of Solar Cycles −3 and −4 are significantly lower than the amplitudes according to the official sunspot number, but they are compatible with sunspot number values obtained from solar activity proxies such as radioisotopes. Our result would imply that solar activity after the Maunder Minimum recovered more gradually and with a lower intensity than previously considered. [ABSTRACT FROM AUTHOR]