Silver was made a common metal after the gold rush of 1848. The silver 3 cent piece or trime was made of 75% instead of 90% silver, making them worth less than face value giving no incentive to melt or hoard them. Also, silver coins from the half dime to the dollar began disappearing from circulation. The influx of silver was undervalued. The trime was introduced to provide a small coin for commerce. Eventually the type two was lightened from 12.375 grains to 11.52 grains. There designs were made. The first 1851-1853 distinguished by no frame around the obverse star. In 1854 the trime was changed to the type II which was made through 1858. The alloy was made to the standard 90% silver and 10% copper as were other silver coins. A raised border was added to the obverse star, on the revers an olive branch and a bundle of arrows were added. This new motif was very difficult to strike up properly. In 1859 the type III was created. Demand was small, after 1862 very few were made. Silver coins were again hoarded by the public and began trading at a premium. In 1873 only proofs were made then the coin was discontinued. Striking on the type I lacked certain details. Sharp coins are rare as the striking quality was was nearly overlooked. Cherry picking is the order of the day. Type II trimes were miserably struck, with most characteristics weak on both sides. Ironically with the lowest mintage, a sharp 1855 is found now and then. Most type III trimes are struck well, with full details observed.
Circulated type I trimes are plentiful with mint state examples often seen. The one branch mint issue 1851-0 is very scarce. Most mint state coins are attractive and lustrous. Circulated type II grades are scarce. Needle sharp grades are rarities. Among type III trimes 1859 to 1862 are easy to find. All later dates are scarce to rare. Gem and mint state coins 1856 and later are very rare. Keep your eyes open, cherry picking again is in order.