If you’ve seen Heads on Sticks within the last year, perhaps you already know David Mueller’s now doing some of his best work with the long-running, ever-evolving outlet of psych-rock, post-punk and dance music. Maybe you even know these songs, as the band issued “Big Decision” and “Surrender” on a limited-edition, tour-only 7-inch last year. They’ve been doing them live, too. But for the set’s new digital version, Heads on Sticks tacked on “The Landscape Vanishes,” another pinnacle of their catalogue. This is a triptych of online riches.

The throbbing “Big Decision” builds tension through repetition, the meter and the riff cycling beneath Mueller’s beguiling mantras. Each shift is like a turn of a relief valve, moved continuously back and forth. “Surrender” is more prismatic, with refracted piano lines settling through an array of scattered drums and distorted bass. The elements eventually coalesce around Mueller’s distant discussion of life lessons and observations; think Wayne Coyne, coming down gracefully, or a blissful hymn from Birds of Avalon, another band in which both Mueller and Heads on Sticks multi-instrumentalist Missy Thangs also play.

But it’s the new addition to the set, “The Landscape Vanishes,” that portends new avenues of exploration for Heads on Sticks. It starts as an amorphous psychedelic fantasy, a saxophone theme shifting and slipping over a syncopated beat. The band charges, though, springing into dance-punk jubilance only to bend out of it again. At one point, they leave nothing but the bass line and the synthesizers hanging, returning to indulge one last gallop. Handclaps and slashing guitar emphasize the hook, sharp enough to be part of Franz Ferdinand’s oeuvre but aloof enough for Mueller’s soft tone.

Heads on Sticks have sometimes obscured their own immediacy. On these three tunes, they know exactly when to hide or highlight it.

This article appeared in print with the headline “Arrivals, departures and Additions.”