In acknowledging the 10th anniversary of Frank Sinatra’s death, Warner Bros. raises its DVD flag to half-mast today with the thrifty release of 13 films, supplemented by few (and in most instances, zero) extra features. The selection covers 23 years (1943-65) in an often feckless Hollywood career that began in 1941 with uncredited vocal cameos and ended resignedly in 1970 save for a halfhearted return a decade later. By then, Sinatra had elected to focus his creative energy on television and records. His film work is often remembered as an adjunct to a musician’s career.

Between 1954 and 1958, though, Sinatra functioned as an actor of nerve, stature, and originality — a natural, perhaps, but also a signature personality playing the type he assiduously perfected onstage. As a quintessential antihero and derisively anti-Method actor, Sinatra — his face filled out with an appealing virility absent in his early years — embraced a work ethic that led to several ambitious movies. In these five years, alongside a couple of middlebrow melodramas, coy comedies, and a fiasco of Himalayan dimensions (“The Pride and the Passion”), he played an assassin in “Suddenly,” the best Nathan Detroit ever in “Guys and Dolls,” a junkie in “The Man With the Golden Arm,” the heir to and equal of Bing Crosby in “High Society,” a semi-heel in “Pal Joey,” and broken men in “The Joker Is Wild” and “Some Came Running.”

By 1956, however, movies had begun to bore him, and tales of his terrible behavior began to circulate: arriving late, not knowing his lines, refusing second takes, refusing to support co-stars in their close-ups. The rest was Rat Pack frivolity, melodramas at which the Sinatra of the ’50s might have rolled his eyes (“The Devil at Four O’Clock”), and unspeakably smarmy comedies (“Marriage on the Rocks”), as Sinatra grew heavy, comfortable, and disengaged. The only high points left were the laconically existential detectives he played in the ’60s, not least the military investigator in “The Manchurian Candidate.”

The Warner Bros. selection is hardly a survey of high points, though it does include his best non-musicals, two indispensable and intricately related works of the ’50s (1955’s “The Man with the Golden Arm” and 1958’s “Some Came Running”), plus the ingenious, if often annoying, postwar musical, “On the Town” (1949). The others? Good lord, Elvis Presley had better vehicles. Some of the early films are salvaged by musical numbers, but as the DVDs lack scene-selection menus, you may develop calluses searching them out.

Sinatra’s first roles came in fussy adaptations of stage plays. He enters 30 minutes into “Higher and Higher” (1943) as a shy neighborhood crooner named Frank Sinatra, whose dreamy “I Couldn’t Sleep a Wink Last Night” shows what the fuss was about. Michelle Morgan batted her eyes and Mel Tormé sang like Sterling Holloway while balancing a pompadour the size of the national debt.

In “Step Lively” (1944), a remake of “Room Service,” Gloria DeHaven looks sexy, George Murphy looks constipated, and Sinatra looks lost. Moviegoers in the ’40s who thought there could never again be an actor as humorless and self-regarding as Murphy must have felt reassured when MGM found Peter Lawford in “It Happened in Brooklyn” (1947).

Make a note regarding the latter: “Time After Time” is at 37:30; the film’s only bolt of energy, Sinatra’s duet with Jimmy Durante, is at 50:20, followed almost immediately by Sinatra and Kathryn Grayson combining anhedonia and chirping in a duet from “Don Giovanni.”

Nothing commends “The Kissing Bandit” (1948) or “Double Dynamite” (1951), a film named for Jane Russell’s double-D dramatic style, which is unaccountably buttoned-up throughout the picture.

These films — and the three musicals with Gene Kelly, boxed separately — come from Sinatra’s monkey period, a reference not to his looks (underfed, abashed and, well, simian), but to the phrase coined by Jerry Lewis to characterize his own roles opposite Dean Martin. Sinatra’s monkey is the virgin shnook who has yet to discover girls, and needs Kelly to set him straight, usually in numbers that find Kelly relentlessly mugging his parodies of women. As the great Durante, whose character in “It Happened in Brooklyn” wears an apron and knits doilies (“derlies”), might have said: “Surrounded by transvestites, dat’s what I am!” The colorful exertions of “Anchors Away” (1945) and “Take Me Out to the Ballgame” (1949) are leached by patriotic piety and sexual arrogance. “On the Town” glories in the wit of an Adolph Green-Betty Comden script, Leonard Bernstein music, and fervent direction by Kelly and Stanley Donen — though even here, Frank looks justifiably humiliated.

After his long winter of discontent (for his 1950 television series, Sinatra wore a mustache and did cutlery commercials), the Chairman remade himself as a recording artist and triumphed with a rather ordinary performance in “From Here to Eternity” (1953). Reborn, he committed himself fully to Otto Preminger’s masterly adaptation of Nelson Algren’s “The Man With a Golden Arm.” Comparisons with Vincente Minnelli’s “Some Came Running,” also starring Sinatra, are diverse — both are based on noted novels, though James Jones’s ambitious and misunderstood 1,266-page anti-epic (which spawned Minnelli’s film) was widely trashed, and has remained unpublished in its entirety for 50 years.

In both films, style and theme are inseparable, and the plotlines reverse the literary fortunes of the protagonists and their wives. Frankie Machine, the card dealer addicted to morphine, and Dave Hirsh, the army vet, writer, and accomplished poker player addicted to self-pity, enter their respective films on buses, returning to Midwestern hometowns; in the end, violence frees them from deceptive women to face uncertain futures. In the novels, Frankie kills his connection and hangs himself, and Dave is shot down at night while leaving town and his monstrous wife. But in the films, suicide, murder, and violent death are reserved for the women.

In Preminger’s film, the monkey is off Frank’s face and on Frankie’s back. Sinatra’s cold turkey is hurried, and the conventions of melodrama demand neat fixes, but the film’s truth resides in the sharp script and a strange mélange of performers who were never better, including Sinatra, Eleanor Parker, Arnold Stang, Darren McGavin, George E. Stone, and even Kim Novak, whose vacant looks and line readings are nonetheless affecting. The virtuoso mobility of Preminger’s camera, sweeping laterally and then down or up before closing in, minimizing edits, demanded of them theatrical concentration. Even the patently phony sound-stage exteriors underscore the power of the actors, emphasizing an unusual merger of theater and cinema.

More than Algren’s novel, Preminger’s film, as written by Walter Newman and Lewis Meltzer, is a study in addiction — heroin addiction is only the most obvious kind. Every character is addicted to something, be it hustling, alcoholism, love, failure, wielding power, getting attention, stealing, gambling, or guilt. They will spin their wheels until they die. In addition to director and cast, the film is stylishly bound by Saul Bass’s animated credits and Elmer Bernstein’s sensational score, which is jazzy but — contrary to critical conventions — not jazz: There is a difference.

The big change introduced in “Some Came Running” by Minnelli and his script writers — John Patrick, whose most creative years coincide with Sinatra’s, and Arthur Sheekman, a Marx Brothers veteran whose career was ending — concerns Ginny, played by Shirley MacLaine in the performance of her life. Jones’s decision to name the novel’s women after oral sex — the psychotically virginal Gwen French and the monstrously dissipated whore Ginny Moorhead — suggests an adolescent japery on par with the author’s decision not to apostrophize contractions. But Minnelli likes Ginny, and allows her to steal the film with a baleful honesty that renders the male characters relatively impotent — Sinatra’s Dave, his pompous brother Frank (superbly played by Arthur Kennedy, who makes the character’s only genuine impulse an act of adultery), and the cynical drifter and misogynist Bama (Dean Martin, born for the role).

Sinatra holds these films together. In “The Man With the Golden Arm,” he is alternately jumpy and smooth, perversely innocent, whistling past the graveyard of his ambition, yet ready at the hint of an obstacle to get lost in drugs. His skin tingles and he is racked with guilt and he lets us see the desperation with a clarity that doesn’t feel like a performance. In “Some Came

Running,” he is comfortable in his skin, yet no less prone to addictive ­alcoholic binges that change Dave so dramatically that Ginny stares at him uncomprehendingly, the way Chaplin’s tramp, in “City Lights,” does the millionaire who is his pal when drunk and dismissive when sober. Sinatra’s strength as Dave is never in doubt, and neither is his infinite capacity for rejection — his sensitivity all but demanding a kind of self-abasement. Has any other actor played quite these notes in quite this way?