Partial independence occurs when one phonemic sequence is independent of another, while the other is not independent of the first. If we break a sequence into two parts, e.g. 'boysenberry' into (/boysƏn/ and /beriy/), and find that in given utterances only one of these parts ever occurs without the other part, we can nevertheless say that each part is a morphemic segment by itself. Thus given /boysƏnberiy/ in 'That’s a rotten boysenberry', we find 'That’s a rotten blueberry', and 'That’s a rotten berry', but we do not find /boysƏn/ next to some sequence other than /beriy/ in this total environment. However, we do find /bluw/ 'blue' next to some sequence other than /beriy/: 'That’s a rotten bluepoint'. In 'That’s a rotten blueberry' we therefore recognize 'blue' and 'berry' as being two independent segments. Hence, in 'That’s a rotten boysenberry', which differs from the preceding utterance only in having /boysƏn/ instead of the independent /bluw/, we must still consider /beriy/ as an independent element. Having done so, we now also recognize /boysƏn/ as a separate element too, since we do not wish to have any sequence of phonemes left over that is not assigned to one element or another. We want to be able to describe a stretch of speech exhaustively as a sequence of morphemes.
- Harris (1951), a pag.177

[…] there may be situations in which we wish to say that a portion of speech which contains an observed segment is represented by absence of a linguistic element. That is, we may take a non-empty stretch of speech and say that it has no independent descriptive status and is in itself represented by no linguistic element, i.e. by a void, or zero, element. All the cases in which this can be done are cases of partial independence, and the effect of this technique is to change these to cases of complete independence.
- Harris (1951), a pag.377