"Did yu: si: mi:." is messy compared to "di.d yu si mi."

Checked vowels can never be the last letter in a word so the only time a free vowel needs to be marked is when it is followed by a consonant. The most elegant solution is to never mark the free vowel.

There are several notations that could be built on this insight. Below, the Checkt Speling© logic is applied to Sweet/Jones broad romic resulting in a notation that is similar in many respects to New Follick (Mont Follick, 1934) and Lindgren's Phonetic A (Harry Lindgren, 1969).

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6 Chekt vowels, 6 Free, 6 Diphthongs, 7 with schwa

Notations don't get much easier than this:
7 vowel letters for 12 pure vowels, 6 combinations, and 7 combinations with R or schwa.

Rationalization
The shwapostrophe is used extensively in this notation. In all cases it refers to a central vowel. Thus u' and a' both refers to a central vowel [uh]. They could both be replaced with a shwapostrope as in 'v (for a'v). With syllabic r l m n, the undenoted shwa is sufficient: 
lita'l --> lit'l --> litl. Reefer/refer = rifr/rif'r or r'fr.

oat --> oa't --> o't This is superior to /ou/ because of the way that TO uses this digraph.
hai lai --> ha'y la'y --> h'y l'y (In Clipt Chekt it is simply hy ly)
break --> brea'k --> bre'k = breik (pattern vein, thei [they])

7 Vowel Letters: aeioury - 15 combinations- a.a a' | e r' ei | i. i y | u. u u' | o. o o'
Many orthographers want to use the most common TO vowel letter and then end up using a digraph. The single letter is always the most common. See frequency studies

Henry Sweet and Daniel Jones had similar minimalist systems as early as 1900. The difference is that they used special characters (notably the turned e, turned c, and turned v) rather than restricting themselves to ASCII characters as has been done with Chekt Speling and SaundSpel. They referred to this notation as broad romic to distinguish it from a narrow IPA transcription.. The basic difference between the two systems was that Jones used an extender mark [:] and Sweet doubled the letters to mark an extended vowel. Sweet used a double schwa for the stressed schwa. Jones used a yogh symbol /3:/. Jones used /^/ for [up] while Sweet used schwa.

In Chekt Speling, the vowel is extended unless marked otherwise with an afterdot. This works out well because the vowels that combine with R are normally long. To show this one has to use aar, iyr, oor... to show the proper pronunciation or add a rule, such as with Nu Speling, that ar is really aar, and or is really aur, and so on.

To serve as a pronunciation guide, all of the light yellow cells (above) need to be marked with a unique symbol. The schemes of Sweet and Jones pass this test. New Spelling almost passes.

The relation between o. and a is so close that they can and have been merged. In such a notation pot is spelled pat and pat is spelled paet or pa.t. It is not merged in CKS because o. is the most common way that TO represents the ah sound. The exception is when ah is combined with R or schwa [ ah+R = ar -- awe+R = or ].

RYMS
squad, swab, mod, 
lawd, laud, maud, fraud, applaud, broad,
lord, board, ore, four, order
lower, oger, ode, cold
nurd, nu'rd, n'rd, abs'rd=absu'rd. sur=sewer su hr
sure sewer - 5ur su'r

Combinations:
ly lyr ly'r (lie, lyre, liar)
ly lyn ly'n (lye, line, lion)
mor, mo'r (more, mower)
mos, cost, cros, ot, cot (moss, cost, cross, ought, caught)
'r, er, e'r, aeroport/a.rport (err, air, error, airport)
hy, hyr, hy'r (hi, high, hier, higher)
ti, tir, ti'r (tea, tear, tearer) no tir ter ambiguity
li.v, lyv, liv, lir (live, live, leave, leer)
loid, loitr, loiyr, loi'l (lloyd, loiter, lawyer, loyal)
te.n, ter, te'r (ten, tear, terror) 
ber, berli, be'r (bare, barely, bearer)
fer, ferli/fe'li, feri/fe'ri/fa.ri, fe'r(fair, fairly, fairy, fairer)
pur, piur, piu'r, endur (poor, pure, purer, endure)
tur, tu'r, turist (tour, tourer, tourist)
taul, taur, flaur (towel, fower, flower)
tol, tor, dor, to'r, bo'tr (tall, tore, door, tower, boater)
lo, lor, lo'r (law, lore, lower) cud bi loa'
bo'a', bor (boa, boor, bore)
peil, feil (pail, pale, fail) the i could also be schwa pe'l

A phoneme that is unmarked is generally merged with some other significant sound. Thus, the vowels in up and ago are often merged. The pure vowel ['r] is often indicated as a diphthong [er or eur] rather than as an extended schwa.
 

Three R-phonemes 1 2 3 r R/@@ @ around her roar @raund hR ro@ In traditional English orthography (TO), three distinct R-sounds are merged. In Cut Spelling, the three distinct sounds are represented by one letter [r]. As shown in the following table, only IPA derived scripts such as Ian's SaundSpel clearly mark the three R related phonemes. The consonant r is usually found in the initial position before a vowel. The syllabic or semi vowel r is usually found in the terminal position following a vowel. The vowel can be the undenoted schwa that is associated with four syllablic consonants. In CKS, rower and roar can be distinguished as ro'r and ror

In most orthographies, combinations are so distorted that they cannot be resolved into their component sounds. When aa is used to represent ah, the R-diphthong for [are] has to be aar. When au is used for awe, the R-diphthong for [or] has to be aur. Most of these orthographies get around the inconsistency by adding a rule.

Turn her around. Turn hur urn uround. (New Spelling)
TRn hR Rn @raund. (SaundSpel) T@@n h@@ @@n @raund. (Sweet's Broad Romic)
T'rn h'r 'rn a'raund. T'rn h'r u'rn a'-raund

There is some ambiguity in CCS since the schwa in [a'raund] could mark either the a or the r: [uh-raund] or [ah-uh-aund]. With [u'rn] it could be [ern] or [uh-uhn]

Sample Sentences
Thei uzd tu h'rl sto'nz o'vr h'r tur bu's.
It woz h'r folt [fo.u'lt], shi left h'r coa't [co't] on x co.t nekst tu x dor.
Th u.ltima't viu iz fr'm th eith flor ov the bilding. 
Hu'ks hu.ks shu.d bi gu.d inu'f tu capchur th bu.l frog.
'I think it w'z during x la.st a'ys eij that wi so x la.st 'v x wu.li ma.ma'th.
Hi geiv hiz w'rd tu x w'rld xa.t ther wu.d bi no wor.