According to the 1969 issue of Conn Chord magazine, the period involving these mouthpieces lasted from 1955 to 1964. In fact, these were probably not produced before 1958 and were produced through at least 1969. As with the Precision mouthpieces, the Improved Precision mouthpieces were the default mouthpieces of the day. Very common.
Quoting the January 1969 issue of Conn Chord magazine: "... the improved Conn "Precision" mouthpieces were designed with matched cup volume and back bore to produce a well-centered, rich tone quality. New design made it possible to hold the taper to a precise tolerance of .005" and produce a lightweight mouthpiece by taking off additional metal." Copyrighted, 1968, By Conn Corp.)
After 1958 the Precision mouthpiece evolved into the "Improved Precision" mouthpiece. See separate entry. There are two ways to tell a Precision mouthpiece from an Improved Precision mouthpiece. First, a precision mouthpiece has vertical lettering, running lengthwise along the shank. An Improved Precision mouthpiece has horizontal lettering, running across the cup. Second, Improved Precision mouthpiece have a rim around the shank; precision mouthpiece don't have this rim.
The following descriptions are from the 1956 accessories catalog.
These description are for cornet; the trumpet mouthpieces are worded slightly differently, but are in fact identical.
Model 1 - Fairly deep, fat bowl with wide rim. Gives full round tone especially on low notes. Comfortable, popular
Model 2 - Same style as bowl No. 1, but the rim is narrower. Excellent for players who want plenty of volume.
Model 3 - Shallow bowl with medium rim. Gives bright quality of tone in all registers. Most popular model.
Model 4 - Same style as No. 3, but with wide rim. Especially comfortable for players with large, full lips.
Model 5 - Small, shallow cup with medium rim. Gives bright tone. Excellent in high register. Popular dance band model.
Model 6 - Extra wide bowl, shallow cup. Rim is narrow and has small throat diameter. Recommended for professionals.
Note that the Improved precision cornet mouthpieces produced from 1955 to 1957 are short shank mouthpieces. These are the occasional "Precision" (not-Improved) mouthpieces you see with horizontal lettering. These are so-called "short shank" cornet mouthpieces. They are ¼" shorter than a modern mouthpiece with a different outside taper of the shank. The modern standard taper is 0.050" per inch. These have a tape of 0.060" per inch." The existence of these mouthpieces, by the way, gives credence to the idea that cornet models produced from 1955 to 1957 took short shank mouthpieces.
Of the above list, the number 4 is by far the most common. The number 5 was apparently standard on the 6B Victor trumpet. I once seen a picture of a Improved Precision Conn 6. I have never seen any of the other models as an Improved Precision mouthpiece (not withstanding Conn's claim that the number 3 was the most popular model).
Model 1 - Fairly deep, fat bowl with wide rim. Gives good clear tone in all registers. Especially suitable for
large bore trombones and symphony work.
Model 2 - Smaller bowl than No.1 and more shallow. Gives big tone, very bright in all registers. Excellent for solo work and for players who want to obtain the high notes with ease.
Model 3 - Slender, deep bowl with wide rim. Gives exceptionally full and round tone in all registers. Especially fine for musicians with large lips.
Model 3A - Slender, smaller bowl with narrower rim. Gives good, round tone in all registers. All around mouthpiece.
Model 4 - For bass trombone. Bowl similar to No.3, but somewhat larger to give full, rich, deep tone quality. Wide rim."
Model 5 - For model 24I
Conn's early 1960's accessories catalog doesn't list model 1 anymore, and model 4 is described as "bass trombone and large bore tenor". As far as I can tell, model 3 is the most common. The model 5 "for 24I (Connstellation)" isn't yet listed in the 1956 accessories catalog because the 24I/25I Connstellation hadn't been developed yet.
Model 1 - For BBb bass. Large, deep bowl with wide rim. Produces exceptionally full, deep, rich tone.
Model 2 - For BBb bass. Large bowl, not as deep as No. 1 . Gives full, rich tone in all registers. Medium rim.
Model 3 - For large Eb bass. Deep bowl with medium rim. Produces full, round tone in all registers.
Model 4 - For small Eb bass. Shallow cup with medium rim. Gives full, rich tone.
The early 1960's accessories catalog lists these as "BBb Bass or Sousaphone, #1, #2" and "Eb Bass, for small bore bass, for large bore bass".
French Horn Mouthpieces
Model 1 - Deep cup.
Model 2 - Medium cup.
Model 3 - Shallow cup.
Compared to the Precision mouthpieces, the descriptions suggest the old model 2 has become the model 3, and a new model 2 has been inserted with a medium cup.
Alto Horn Mouthpieces
Model 1 - Deep cup, medium rim.
Model 2 - Fairly shallow cup, medium rim. Somewhat brighter than No. 1.
Model 3 - French horn cup and rim
New compared to the 1938 catalog in this list is model 3.
Model 1 - Mellophone model with deep cup.
Model 2 - Mellophone model with shallow cup.