Direct interface circuits are a simple, inexpensive alternative for the digital conversion of a sensor reading, and in some of these circuits only passive calibration elements are required in order to carry out this conversion. In the case of resistive sensors, the most accurate methods of calibration, namely two-point calibration method (TPCM) and fast calibration methods I and II (FCMs I and II), require two calibration resistors to estimate the value of a sensor. However, although FCMs I and II considerably reduce the time necessary to estimate the value of the sensor, this may still be excessive in certain applications, such as when making repetitive readings of a sensor or readings of a large series of sensors. For these situations, this paper proposes a series of calibration methods that decrease the mean estimation time. Some of the proposed methods (quasi single-point calibration methods) are based on the TPCM, while others (fast quasi single-point calibration methods) make the most of the advantages of FCM. In general, the proposed methods significantly reduce estimation times in exchange for a small increase in errors. To validate the proposal, a circuit with a Xilinx XC3S50AN-4TQG144C FPGA has been designed and resistors in the range (267.56 Ω, 7464.5 Ω) have been measured. For 20 repetitive measurements, the proposed methods achieve time reductions of up to 61% with a relative error increase of only 0.1%.