Three reactor types can be designed with pebbles (carbon spheres) as the reactor core: the pebblebed high-temperature gas-cooled reactor (PB-HTGR), the pebble-bed fluoride-salt-cooled high-temperature reactor (PB-FHR), and the thermal-spectrum molten salt reactor (MSR) with fuel dissolved in coolant. In the HTGR and FHR, the pebbles are fuel (coated-particle fuel) and moderator (graphite). In a MSR the pebbles would be the moderator (no fuel). Recent advances enable prediction and modeling of pebble beds with two or more sizes of pebbles. This may enable the use of pebble beds with multiple size pebbles that create new options. A second smaller size of HTGR/FHR fuel pebble that fills some of the space between the regular pebbles can increase the power output for the same size reactor. For the FHR the second pebble size would reduce inventory of expensive coolant and may widen choices of salt coolants. In an HTGR or FHR, smaller pebbles with high actinide loadings and high heat transfer rates could be used to burn actinides while the larger pebbles are the driver fuel. Multiple pebble sizes in MSRs may enable varying the carbon-to-fuel ratio to optimize the neutron spectrum over time to more efficiently utilize the fuel and allow easy replacement of moderator. The smaller pebbles with no fuel and a high surface-to-volume ratio could be designed to remove (1) HTGR/FHR/MSR tritium from the coolant and (2) noble metal fission products and potentially other impurities in MSRs. We examine the potential incentives for pebble beds with multiple size pebbles. With the tools now available to quantify pebble-bed behavior with multiple size pebbles, the next step is to begin to quantify benefits and limitations for different applications of pebble-bed reactors with multiple sizes of pebbles. Keywords-Fluoride-salt-cooled high-temperature reactor, molten salt reactor, high-temperature gas-cooled reactor, pebble-bed reactor. Note-Some figures may be in color only in the electronic version.