The British achieved the apex of military muzzleloading ammunition with the invention of the ammunition for the Enfield family of muskets. Started with the Pattern 1851, and refined with the Pattern 1853, the cartridge featured a integrated paper-patched bullet. The bullet was made from pure lead and smooth-sided.
The first bullet, the "Pritchett" bullet, had a small cavity in the base. This was not so much for expansion as a place to fold the paper for the bottom of the cartridge, and possibly to shift the center of gravity slightly forward. The Pritchett bullet obdurated by compression more than expansion.
It was discovered that the .568" diameter Pritchett bullet (before paper) was difficult to load with service ammunition on fouled bores. Worse, if the bullets were sized at their minimum tolerance (.566) and musket bores were at their maximum tolerance, the Pritchett design could not expand enough to take up the rifling. This was a disaster that almost ended the P1853 musket.
The solution was the Hay bullet, which was still .568" in diameter (before paper), but now had deep internal cavity into which a hemispherical iron cup was placed. This was soon discarded for a truncated cone iron cup, which was almost immediately replaced by a truncated wooden plug made from Boxwood.
These bullets still proved difficult to load in the field on fouled guns with service ammunition that had been shipped by sea and overland by wagon in extreme weather conditions.
The final iteration came with an extreme solution brought forth by Boxer (the same Boxer who gave us Boxer primers). He reduced the size of the bullet to .550"! Despite fears that such a massively undersized bullet would not be accurate, or even fall out of the barrel, it turned out to be at least as accurate as the previous Hay bullet.
Final tweaks to the design included changing the wooden plug to a fired clay plug, and changing the lubricant (anti-fouling agent, really) from a mixture of tallow and beeswax to pure beeswax. It was found that the acids in the tallow oxidized the lead bullet, causing to increase slightly in size.
Here is a video that talks about the 3 bullet variants: