What does the abbreviation 'compl.' mean in the Oxford English Dictionary (OED)

*Note: One might (understandably) think my question off-topic because the OED should list the abbreviations it uses, and if not, surely Google will have the answer. Please bear with me while I explain.*

I wanted to learn more about the word, bespeak, so I turned to the venerable Oxford English Dictionary (OED).¹ Definition number 7 for bespeak reads in part:²

7.

a. To speak of, tell of, be the outward expression of; to indicate, give evidence of.

1629 J. Earle Micro-cosmogr. (ed. 5) xx. sig. E2v His very countenance and gesture bespeak how much he is.

1814 Wordsworth Excursion i. 42 But her House Bespake a sleepy hand of negligence. 1863 C. C. Clarke Shakespeare-characters iii. 65 Hamlet's proneness to soliloquy bespeaks the reflective man.

b. with compl.

a1704 T. Brown Oration in Praise Drunkenness in Wks. (1707) I. i. 47 Such whose smiling Aspect bespeaks them Friends.

1815 Scribbleomania 18 Symptoms bespeaking me rash.

QUESTION: What does 'compl.' mean in definition 7b?

My Research

I looked for a list of abbreviations in the OED itself, but if it's there, I could not find it.
I Googled "compl." (with and without the quotation marks);
I Googled ("compl." AND abbreviation) - with and without the parentheses;
I searched several abbreviation sites; and
I reviewed publishing terms and their abbreviations in the BlueBook (citation guide for law reviews and other legal writing).

What I learned

In the publishing world, 'comp.' stands for compilation or compile.³
In the legal world, 'compl.' stands for complaint.
AcronymFinder indicates that 'compl' stands for complete or completion.
AllAcronyms.com informed me that 'comp.' can refer to compound or composition.
TheFreeDictionary.com instructed me that 'compl' refers to a 1966 article in The Computer Journal, titled "The COMPL Language and Operating System". 4

Unfortunately, I did not learn what the OED means by 'compl.'

~ Mark

Footnotes

Subscription required. However, most university and public libraries provide their members with access to OED Online. There are also the Oxford Dictionaries, abbreviated ODO (Oxford Dictionary Online). The URL for Oxford Dictionary - English is https://en.oxforddictionaries.com/
'in part' - I did not include all the examples of historical usage (quotations) because the OED (print or online) is protected by copyright, therefore I did not want to copy and paste the entire definition verbatim.
The Bluebook: A Uniform System of Citation 517 tbl.T.14 (Columbia Law Review Ass’n et al. eds., 20th ed. 2015).
A. G. Fraser, J. D. Smart; The COMPL Language and Operating System. Comput J 1966; 9 (2): 144-156. doi:10.1093/comjnl/9.2.144

Answering my own question because I finally found it!

Google came to the rescue when it located The Oxford English Dictionary: List of Abbreviations on the Indiana University website--posted 21 years ago!

I eventually also found the OED abbreviation list on the OED website. (Their site would benefit from some user testing...).

The Answer

In the OED, 'compl.' stands for complement.

What does complement mean in this context?

Here is the relevant definition of complement from the OED:

b. Grammar. One or more words joined to another to complete the sense (see quots.).

1876 C. P. Mason Eng. Gram. (ed. 21) §391 Many verbs do not make complete sense by themselves..and the words used with them to make predication complete may be called the complement of the predicate.

1964 E. Palmer tr. A. Martinet Elements Gen. Linguistics iv. 11
Hier, il y avait fête au village...hier and au village..may be eliminated without the utterance ceasing to be a normal sentence..and this is what is meant by the traditional terminology which speaks of them as ‘complements’.

In-depth discussion about complements (grammar)

TheFreeDictionary.com offers the following definition, along with an extensive discussion of the different types of complements (in the grammatical sense).

Complements are words or groups of words that are necessary to complete the meaning of another part of the sentence. Complements act like modifiers to add additional meaning to the word or words they are attached to. However, unlike adjunct modifiers, they do not add supplemental information—they provide information that is necessary to achieve the intended meaning in the sentence.

If English is your second language...

Note that complement and compliment are sometimes confused. They are two different words, with different meanings.