i before e except after c exceptions

The one I always remember is weird, but it turns out there are many exceptions to the rule "i before e except after c".

Here is a list:
beige, cleidoic, codeine, conscience, deify, deity, deign,
dreidel, eider, eight, either, feign, feint, feisty,
foreign, forfeit, freight, gleization, gneiss, greige,
greisen, heifer, heigh-ho, height, heinous, heir, heist,
leitmotiv, neigh, neighbor, neither, peignoir, prescient,
rein, science, seiche, seidel, seine, seismic, seize, sheik,
society, sovereign, surfeit, teiid, veil, vein, weight,
weir, weird

Also:
This list could obviously be extended by adding more derivatives of Latin "scire", and by adding inflected forms of some of the basic words listed. The list has "conscience", "prescient", and "science", but there are also, for example, "omniscient" and "nescient". To "eight" could be added "eighty", "eighteen", and "eighth". And the list could be greatly extended by adding the plurals of all words ending in "cy".

(Is someone going to cite a word ending in "cy" that doesn't form its plural with "cies"? I can't think of any at the moment, given that I'm excluding capitalized words from my discussion.)

With regard to the extension added by some people for "neighbor" and "weigh", and the fact that this is only a start toward covering all the sounds of "ei", I have broken down my list according to the six different sounds "ei" had in that list. In doing so I have excluded cases where the "ei" or "ie" was not a digraph. Here is the list as so reorganized:

It seems the exceptions almost outweigh the rule. But I often fiend it useful to remember when writing words like receive, retrieve etc.

Sources:
http://alt-usage-english.org/I_before_E.html