The psychophysical methods were developed by Fechner to find out the perceptual threshold of a stimulus, that is, the weakest stimulus that could be perceived. In spite of the strong efficiency in measuring thresholds, psychophysics does not help to define the multiplicity and complexity of possible percepts emerging from the same stimulus conditions, and accordingly, of what we perceive. In order to define what we perceive it is also necessary to define what we can perceive within the multiplicity of possible visual outcomes and how they are reciprocally organized. Usually the main experimental task is aimed at focusing on the specific attribute to be measured: what comes before psychophysics, i.e., the phenomenological exploration, is typically not fully investigated either epistemologically or phenomenally, even if it assumes a basic role in the process of scientific discovery. In this work, the importance of the traditional approach is not denied. Our main purpose is to place the two approaches side by side so that they complement each other: the phenomenological exploration complements the quantitative psychophysical measurement of the qualities that emerge through the preliminary exploration. To demonstrate the basic role played by the phenomenological exploration in complementing the psychophysical investigation we introduce three critical visual conditions, called visual gradient of perceptibility, perceptible invisibility and visual levels of perceptibility. Through these conditions several new illusions are studied and some phenomenological rules are suggested.