In fact, the use of the factor of 10 in the definition of the decibel is to create a unit which is about the least detectable change in sound intensity.
That having been established, it can be noted that there are some variations. The jnd is about 1 dB for soft sounds around 30-40 dB at low and midrange freqencies. It may drop to 1/3 to 1/2 a decibel for loud sounds.
Caution must be used in applying the "one decibel" criterion. It presumes that you are increasing the same sound by one decibel. If you were adding a sound outside the critical band of frequency from this sound, you would be exciting fresh nerve endings, and the one decibel rule can't be presumed to apply. This causes some concern about the perceptual encoding schemes used with modern digital recording which might eliminate some significant audible content by the use of a "one decibel" criterion for dropping content.