Recently I promised a couple of forum members to put together a family photo of some .32 Target Revolvers. Here is a snapshot showing some specimens I had available.
Top, l. to r.: 2nd model .32 HE, 1904 (one of only two nickel target .32s known from this era); Regulation Police target, 1923; Regulation Police Target, 1919; Regulation Police Target, 1957 (postwar production, but incorporating many prewar parts; only 196 produced).
Second row, l. to r. If I hadn't grabbed the wrong gun from my sorting shelf, that first gun would be a 1949 K-32 Masterpiece; the second gun is a legitimate K-32 Masterpiece from 1949; the third gun is a Colt .32 Officers Model Target from 1940 that I added to this picture on the principle of general scarcity: Colt actually built fewer .32 Target models on the Army Special frame than than S&W built K-frame .32s.
The K-frame on the left is not the K-32 I thought I was arranging, but a wide-rib K-38 from 1950. Embarrassment! Somewhere in the safe there is actually another 1949 K-32, probably in a gun sock that labels it as a K-38. I will retake this family photo and replace this image when I have the chance.
If you stop to think about early models with adjustable sights, some interesting proportions emerge. In I-frames, S&W produced about 258000 .32 units between 1903 and 1917 -- the run of the .32 HE, Second Model. With the exception of a thousand units or so, and perhaps not more than several hundred, these guns all had fixed sights. Target .32s seem to constitute less than one half of one percent of total output. Similarly, the .32 HE third model, in which we must number the square butt Regulation Police variety introduced in 1917, use up serial numbers between about 258000 and 535000. No round butt .32 target configurations are known from this period, and all .32 targets were marketed as .32 Regulation Police Target Revolver. Again, perhaps no more than a thousand out of well over a quarter of a million were produced with adjustable sights -- again, less than one half of one percent.
Interestingly, when S&W chose to put out a .22 version of the I-frame (the .22/32 Heavy Frame Target and its shorter barrel relative, the .22/32 Kit Gun) they did not produce a single one with fixed sights. I think total production of .22/32 revolvers in the prewar years cannot exceed 25000; so about five percent of all I-frames produced in the .32 HE Second and Third model numbering sequence were actually .22 revolvers with adjustable sights.
As a footnote, S&W seems never to have produced a .38 Regulation Police revolver with adjustable sights. I suspect that such specimens may exist, but they would have been a special order from the factory or possibly an aftermarket conversion by a gunsmith.
In K-frames, we know that total K-32 Masterpiece production amounted to a little over 3600, both Pre 16 and Model 16 taken together. I leave out the 16-4, which is uncommon enough in its own right, but is also different enough to be a separate model in my mind.
Production statistics on Colt target .32s are not completely clear to me, but the .32 Officers Model target, which is roughly the equivalent of the K-32, may exist in no more than a thousand copies. Though harder to find than K-32s, they are not yet as expensive (or weren't a year ago, which is the last time I looked at them as a group).

Top, l. to r.: 2nd model .32 HE, 1904 (one of only two nickel target .32s known from this era); Regulation Police target, 1923; Regulation Police Target, 1919; Regulation Police Target, 1957 (postwar production, but incorporating many prewar parts; only 196 produced).
Second row, l. to r. If I hadn't grabbed the wrong gun from my sorting shelf, that first gun would be a 1949 K-32 Masterpiece; the second gun is a legitimate K-32 Masterpiece from 1949; the third gun is a Colt .32 Officers Model Target from 1940 that I added to this picture on the principle of general scarcity: Colt actually built fewer .32 Target models on the Army Special frame than than S&W built K-frame .32s.
The K-frame on the left is not the K-32 I thought I was arranging, but a wide-rib K-38 from 1950. Embarrassment! Somewhere in the safe there is actually another 1949 K-32, probably in a gun sock that labels it as a K-38. I will retake this family photo and replace this image when I have the chance.

If you stop to think about early models with adjustable sights, some interesting proportions emerge. In I-frames, S&W produced about 258000 .32 units between 1903 and 1917 -- the run of the .32 HE, Second Model. With the exception of a thousand units or so, and perhaps not more than several hundred, these guns all had fixed sights. Target .32s seem to constitute less than one half of one percent of total output. Similarly, the .32 HE third model, in which we must number the square butt Regulation Police variety introduced in 1917, use up serial numbers between about 258000 and 535000. No round butt .32 target configurations are known from this period, and all .32 targets were marketed as .32 Regulation Police Target Revolver. Again, perhaps no more than a thousand out of well over a quarter of a million were produced with adjustable sights -- again, less than one half of one percent.
Interestingly, when S&W chose to put out a .22 version of the I-frame (the .22/32 Heavy Frame Target and its shorter barrel relative, the .22/32 Kit Gun) they did not produce a single one with fixed sights. I think total production of .22/32 revolvers in the prewar years cannot exceed 25000; so about five percent of all I-frames produced in the .32 HE Second and Third model numbering sequence were actually .22 revolvers with adjustable sights.
As a footnote, S&W seems never to have produced a .38 Regulation Police revolver with adjustable sights. I suspect that such specimens may exist, but they would have been a special order from the factory or possibly an aftermarket conversion by a gunsmith.
In K-frames, we know that total K-32 Masterpiece production amounted to a little over 3600, both Pre 16 and Model 16 taken together. I leave out the 16-4, which is uncommon enough in its own right, but is also different enough to be a separate model in my mind.
Production statistics on Colt target .32s are not completely clear to me, but the .32 Officers Model target, which is roughly the equivalent of the K-32, may exist in no more than a thousand copies. Though harder to find than K-32s, they are not yet as expensive (or weren't a year ago, which is the last time I looked at them as a group).
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