What kind of packages can utilize the non-machinable surcharge?

The non-machinable surcharge applies specifically to packages with odd shapes. This is because such packages cannot be processed through automated sorting machines, which can lead to additional handling and processing costs for the Postal Service. Consequently, they incur a surcharge to account for this extra manual work.

Lightweight packages and those sent via Priority Mail may still fall under standard processing categories unless they possess odd shapes, which would not typically trigger the non-machinable surcharge criterion. Packages that fit specific dimensions and shapes determined by the Postal Service might not incur this additional cost if they can be processed through normal channels. Thus, the correct answer focuses on the unique characteristics of packages that disrupt standard handling processes.