The current differential diagnosis for a short child with low insulin-like growth factor I (IGF-I) and a normal growth hormone (GH) peak in a GH stimulation test (GHST), after exclusion of acquired causes, includes the following disorders: (1) a decreased spontaneous GH secretion in contrast to a normal stimulated GH peak (“GH neurosecretory dysfunction,” GHND) and (2) genetic conditions with a normal GH sensitivity (e.g., pathogenic variants of <i>GH1</i> or <i>GHSR</i>) and (3) GH insensitivity (GHI). We present a critical appraisal of the concept of GHND and the role of 12- or 24-h GH profiles in the selection of children for GH treatment. The mean 24-h GH concentration in healthy children overlaps with that in those with GH deficiency, indicating that the previously proposed cutoff limit (3.0–3.2 μg/L) is too high. The main advantage of performing a GH profile is that it prevents about 20% of false-positive test results of the GHST, while it also detects a low spontaneous GH secretion in children who would be considered GH sufficient based on a stimulation test. However, due to a considerable burden for patients and the health budget, GH profiles are only used in few centres. Regarding genetic causes, there is good evidence of the existence of Kowarski syndrome (due to <i>GH1</i> variants) but less on the role of <i>GHSR</i> variants. Several genetic causes of (partial) GHI are known (<i>GHR</i>, <i>STAT5B</i>, <i>STAT3</i>, <i>IGF1</i>, <i>IGFALS</i> defects, and Noonan and 3M syndromes), some responding positively to GH therapy. In the final section, we speculate on hypothetical causes.