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The discovery of a previously unrecognized source of spurious signals in observations of the 21-cm Zeeman effect in HI emission features was reported at the Berkeley meeting. Results are presented of observations made since then with the NRAO 140-ft telescope in 37 directions in which other workers claimed to have detected magnetic fields. For 28 directions it was found that the apparent Zeeman effect signals were invariably produced by interaction between polarized beam structure (PBS) and emission brightness variations around the source. By using profile shapes observed near the source directions, first-order corrections for sidelobe signals were applied to the data, after which evidence for the apparent Zeeman effect signals disappeared. In the other 9 directions tested, no Zeeman effect was observed, even in the uncorrected data. It is concluded that no magnetic fields have yet been detected in HI emission features. A review of all available data, including extensive mapping observations made with the 140-ft during the last several years, which have been corrected for PBS artefacts, shows that the fields in HI emission structures are generally <2 microGauss. In the HI toward MBM40, the line-of-sight field is as low as 0.49 microGauss. In order to detect fields in the microGauss regime without resorting to corrections to the data, PBS will have to be reduced to 0.02%, an order of magnitude lower than has so far been achieved. In the meantime, PBS must be mapped and convolved with HI brightness structure around the source to determine whether putative signals are artefacts of imperfect feed characteristics. Until this is done, claims of Zeeman effect detections in HI emission features (and probably OH emission as well) based on observations made with presently available single-dish radio telescopes cannot be regarded as reliable.