The proximate origins of morphemic analysis lie in the work of Leonard Bloomfield, though Bloomfield’s approach served more as a source of inspiration than as an explicit model of analysis. The two most consequential aspects of Bloomfield’s model are the dissociation of lexical form from grammatical arrangement and the recognition of a separate component, termed the ‘lexicon’, which consists, at least for the most part, of minimal lexical forms: 
A linguistic form which bears no partial phonetic-semantic resemblance to any other form, is a simple form or morpheme ... The total stock of morphemes in a language is its lexicon. (Bloomfield 1933: i6if.)
It is natural for a contemporary reader to interpret this passage in the context of a hierarchy of linguistic levels, one in which phonemes are combined to form morphemes, morphemes are combined to form words, words are combined to form phrases, and so on. However, this construal is anachronistic, anticipating revisions that would appear later, in the work of Bloomfield’s successors. The initial Bloomfieldian conception is more intricate and, in many ways, closer in character to contemporary construction-based and discriminative approaches.
The most novel—and difficult—aspect of this model involves the relation between ‘forms’ and ‘arrangements’. Arrangements are the more transparent notion, corresponding to something like ‘dimensions of grammatically distinctive variation’ Of the four types of arrangement that Bloomfield distinguished, three (‘order, ‘modulation’ and ‘modification’) are relatively straightforward:
The meaningful arrangements of forms in a language constitute its grammar. In general, there seem to be four ways of arranging linguistic forms. (1) Order is the succession in which the constituents of a complex form are spoken... (2) Modulation is the use of phonemes which do not appear in any morpheme, but only in grammatical arrangements of morphemes... (3) Phonetic modification is a change in the primary phonemes of a form... (4) Selection of forms contributes a factor of meaning because different forms in what is otherwise the same grammatical arrangement, will result in different meanings. (Bloomfield 1933:163b)
The linear order of formatives is an obvious dimension of variation, as are the suprasegmental properties (such as stress or intonation) that Bloomfield subsumes under modulation. His notion of phonetic modification likewise encompasses a range of contextually-conditioned phenomena, including devoicing or sandhi patterns. It is the notion of ‘selection’ that gives Bloomfield’s model its distinctive character. The basic idea is simple, and even familiar to those accustomed to thinking in construction-based terms. Rather than treating forms solely as the sum of independently assembled parts, the Bloomfieldian model integrates a ‘top- down’ perspective in which constructions are described in terms of characteristic choices of components. The reason that this is not merely a different perspective on the ‘bottom-up’ assembly of forms from minimal elements is that selection is associated with a meaning component (what Bloomfield calls an ‘episememe’) which is in addition to the meanings contributed by the parts selected (which he terms ‘sememes’):
The features of grammatical arrangement appear in various combinations, but can usually be singled out and separately described. A simple feature of grammatical arrangement is a grammatical feature or taxeme. A taxeme is in grammar what a phoneme is in the lexicon—namely, the smallest unit of form. Like a phoneme, a taxeme, taken by itself, in the abstract, is meaningless. Just as combinations of phonemes or, less commonly, single phonemes, occur as actual lexical signals (phonetic forms), so combinations oftaxemes, or, quite frequently, single taxemes, occur as conventional grammatical arrangements, tactic forms. A phonetic form with its meaning is a linguistic form; a tactic form with its meaning is a grammatical form. When we have occasion to contrast the purely lexical character of a linguistic form with the habits of arrangement to which it is subject, we shall speak of it as a lexical form. In the case of lexical forms we have defined the smallest meaningful units as morphemes, and their meanings as sememes; in the same way, the smallest meaningful units of grammatical form may be spoken of as tagmemes, and their meanings as episememes. (Bloomfield 1933:166)
Bloomfield’s obscure terminology makes an already difficult conception even more challenging. However, the key feature of this conception is that meaningful ‘units of form’ are not just ‘chunks’ of segmental material, but include any distinctive characteristics that can be abstracted from a form. It is of course possible to think of minimal lexical forms, i.e. ‘morphemes’ as being represented (and, possibly, stored) independently of the larger forms from which they are abstracted. But it is not possible to conceive of minimal units of grammatical form, i.e. ‘tagmemes, in the same way. In later Post-Bloomfieldian accounts, the notion of selection is encapsulated in rules or complex lexical entries. But Bloomfield describes selectional taxemes with reference to forms or construction types that exhibit them. It is therefore misleading to think of Bloomfieldian analysis as consisting of the disassembly of complex forms into minimal units of lexical and grammatical form, and the assignment of these units to separate lexical and grammatical inventories. Analysis is more a process of classification in which complex forms perform a dual function, providing the data to which procedures of analysis are applied, and at the same time serving as the repository of units of grammatical form.
-  The creeping tendency to conflate ‘morphs’ (units of form) with ‘morphemes’ (units of meaning)reinforces the impression that the identification of morphemes is essential to an analysis of thedistribution and variation exhibited by morphs.
-  The postulation of a separate lexicon was accompanied by the claim that this lexical repository waslargely free of patterns or ‘redundancy, i.e., that “the lexicon is really an appendix of the grammar, a listofbasic irregularities” (Bloomfield Г933:274).