Cory and Ritchey* introduced a very simple, clever method to suppress background signals in 1988. Their method uses a composite pulse, consisting of a 90° and two 180° pulses with appropriate phase cycling, in place of a conventional 90° pulse. The phase cycled composite pulse is essentially a 90° pulse for all spins inside the coil and 0° for all spins outside of the coil. An example of its implementation is shown in the figure below.
The bottom traces show the 11B [1H] NMR spectra for a dilute sample of NaBH4 and a "real" synthetic sample on the left and right, respectively. One can see an enormous background signal from both the NMR probe and the NMR tube. In the case of the "real" synthetic sample, the information from the spectrum is difficult or impossible to recover. The top traces show similar spectra acquired using the composite pulse. The only background signal remaining is that from the portion of the NMR tube inside the coil. This pulse sequence (without proton decoupling) is in the Bruker pulse program library called "zgbs". It is not exclusive to 11B.D.G. Cory and W.M. Ritchey. Journal of Magnetic Resonance, 80, 128 (1988).

The bottom trace shows a single scan 13C NMR spectrum of a concentrated solution of menthol in CDCl3 after the sample had sat in the magnet for a minute or so. The top trace shows a similar single scan acquisition preceded by 16 dummy scans. The relaxation delay was set to 1 second and the acquisition time for the FID was 1 second. 90° pulses were used in both spectra. One can see that some of the resonances in the top spectrum are attenuated in comparison to the bottom spectrum. The 13C signal from the CDCl3 (which has a long T1) is missing in the spectrum acquired with dummy scans. The dummy scans have selectively presaturated the solvent.