With all possible speed

• Lickety-split
• With great speed
• Snappily, say
• Quickly
• Quickly running past those
• With immediacy, or a hint to the four other longest puzzle answers

Douglas Harper's Etymology Dictionary Word definitions in Douglas Harper's Etymology Dictionary
1590s, from a noun (1530s) meaning "great speed," usually said to be from "post haste" instruction formerly written on letters (attested from 1530s), from post (adv.) + haste (n.). The verb post "to ride or travel with great speed" is recorded from 1550s. ...

Wikipedia Word definitions in Wikipedia
Posthaste is the second studio album by the band OHMphrey , released on April 10, 2012 through Magna Carta Records . It features two additional live tracks that were recorded at Winston's in San Diego, California from a concert in 2009.

Wiktionary Word definitions in Wiktionary
adv. quickly, as fast as someone travelling post; with great speed n. (alternative spelling of post-haste English)

The Collaborative International Dictionary Word definitions in The Collaborative International Dictionary
Posthaste \Post`haste\, adv. With speed or expedition; as, he traveled posthaste; to send posthaste. --Shak.