For a given (fixed) set of constraints:

1. Manufacturer,
2. Manufacturing technology,
3. Dielectric type,
4. Target application, i.e.: decoupling, general purpose, high-frequency or power line filtering,
5. Mounting style, i.e.: SMD, through-hole or chassis,
6. Ccapacitance value,

The only feature that requires increasing the size of a capacitor is its voltage rating.

Reasoning the other way around,

You can trade off a smaller voltage rating of the capacitors in your design for a smaller package size (assuming the set of constraints above).

For a given (fixed) set of constraints:

1. Manufacturer,
2. Manufacturing technology,
3. Dielectric type,
4. Target application, i.e.: decoupling, general purpose, high-frequency or power line filtering,
5. Mounting style, i.e.: SMD, through-hole or chassis,
6. Capacitance value,

The only feature that requires increasing the size of a capacitor is its voltage rating.

Reasoning the other way around,

You can trade off a smaller voltage rating of the capacitors in your design for a smaller package size (assuming the set of constraints above).