Astronomic line mapping with single-pixel instruments is usually performed in an on-the-fly (OTF) or a raster-mapping mode depending on the capabilities of the telescope and the instrument. The observing efficiency can be increased by combining several source-point integrations with a common reference measurement. This is implemented at many telescopes, but a thorough investigation of the optimum calibration of the modes and the best way of performing these observations is still lacking. We use knowledge of the instrumental stability obtained by an Allan variance measurement to derive a mathematical formalism for optimizing the setup of mapping observations. Special attention has to be paid to minimizing of the impact of correlated noise introduced by the common OFF integrations and to the correction of instrumental drifts. Both aspects can be covered using a calibration scheme that interpolates between two OFF measurements and an appropriate OFF integration time. The total uncertainty of the calibrated data consisting of radiometric noise and drift noise can be minimized by adjusting the source integration time and the number of data points observed between two OFF measurements. It turns out that OTF observations are very robust. They provide a low relative noise, even if their setup deviates considerably from the optimum. Fast data readouts are often essential to minimize the drift contributions. In particular, continuum measurements may be easily spoiled by instrumental drifts. The main drawback of the described mapping modes is the limited use of the measured data at different spatial or spectroscopic resolutions obtained by additional rebinning. Comment: Accepted for publication in Astronomy & Astrophysics