This discography was sent to me by Steve Goulding, but credits must go to Johannes Deininger, cause he did the work.
You may be interested in Graham Parker, then go to Johannes' Graham Parker homepage.

Part 1: Rumour singles and albums
Part 2: Graham Parker singles
Part 3: Graham Parker albums

(*) Track not to be found (in this form) on a regular album
(**) Track not to be found on a regular album or on a compilation

Rumoursingles and albums

MAX
(Vertigo 6360 149, 7/1977, UK)
(Mercury 1977, USA)
Produced by Robert John Lange and The Rumour
Mixed by The Rumour
Recorded at Rockfield Studios Monmouth
Mixed at Wessex Studios London
Engineers: Ted Sharpe (Rockfield), Tim Friese-Greene (Wessex)
Side 1: Mess With Love / Hard Enough To Show / Do Nothing 'Till You Hear From Me / Jet Plane / Looking After No. 1
Side 2: I'm Gonna Make You Love Me / I'm So Glad / Face To Face / This Town / Somethin's Goin' On

I'M SO GLAD b/w THIS TOWN
(Vertigo 6059 181 (7"), 10/1977, UK)

FROZEN YEARS b/w ALL FALL DOWN
(Stiff BUY 43 (7"), 2/23/1979, UK)

FROZEN YEARS (Edited Version) b/w ALL FALL DOWN
(Stiff promo (7"), 1979, UK)

FROGS, SPROUTS, CLOGS AND KRAUTS
(Stiff SEEZ 13, 3/1979, UK) Produced by The Rumour and Roger Bechirian
Recorded at Eden
Mixed at Eden and Wessex
Engineers Roger Bechirian and someone at Wessex
Side 1: Frozen Years / Emotional Traffic / Tired Of Waiting / Loving You (Is Far Too Easy) / Euro Side 2: Leaders / We Believe In You/New Age / All Fall Down / One Good Night / I Can't Help Myself
Bonus tracks on CD reissues
(Repertoire REP 4219-WY, 1991, Germany, and
Disky STIFFCD 01, 1993, Holland):
Hard Enough To Show / Frozen Years (Edited Version) / I Want To Make You Very Happy (as "The Duplicates") / Call Of The Faithful (as "The Duplicates")

FROGS, SPROUTS, CLOGS AND KRAUTS
(Arista AB 4235, 1979, USA)
Side 1: Emotional Traffic / We Believe In You/New Age / Frozen Years / Tired Of Waiting / Euro
Side 2: One Good Night / Loving You (Is Far Too Easy) / All Fall Down / Leaders / I Can't Help Myself
EMOTIONAL TRAFFIC b/w HARD ENOUGH TO SHOW
(Stiff BUY 45 (7"), 5/1979, UK)
(Arista AS 0451 (7"), 1979, USA)

As "The Duplicates:"
I WANT TO MAKE YOU VERY HAPPY b/w CALL OF THE FAITHFUL
(Stiff BUY 54 (7"), 1979, UK)

PURITY OF ESSENCE
(Stiff SEEZ 27, 7/1980, UK)
Produced and engineered by Alan Winstanley, assisted by Neil King Recorded at Eden Studios and Genetic Sound
Side 1: Little Red Book / I Don't Want The Night To End / Have You Seen My Baby / Falling In Love With A Dream / Tula
Side 2: Writing In The Water / Houston / It's Gonna Work Out Fine / More Than She Will Say / Pyramids / That's The Way The Ball Rolls
Bonus track on CD reissues (Disky STIFFCD 14, 1993, Holland, and Gadfly 227, 3/25/1997, USA): Name & Number

MY LITTLE RED BOOK b/w NAME AND NUMBER
(Stiff BUY 81 (7"), 1980, UK)

I DON'T WANT THE NIGHT TO END b/w PYRAMIDS
(Stiff BUY 92 (7"), 9/1980, UK)

PURITY OF ESSENCE
(Hannibal 1981, USA)
No producer credited
Engineered by John Wood and Bill Gill
Recorded at Island Studios, Hammersmith
Side 1: Tula / I Don't Want The Night To End / Writing In The Water / All Boys Lie / Have You Seen My Baby / Rubber Band Man
Side 2: More Than She Will Say / Houston / Falling In Love With A Dream / Depression / I Think It's Gonna Work Out Fine / Name And Number

Graham Parker singles

SOUL SHOES b/w WHITE HONEY
(Vertigo 6059 147 (7"), 7/1976, UK)

SOUL SHOES b/w YOU'VE GOT TO BE KIDDING
(Mercury 73834 (7"), 1976, USA)

SOUL SHOES (edit, 3:03) (**) b/w SOUL SHOES (edit, 3:03) (**)
(Mercury DJ463 (promo 7"), 1976, USA)

SILLY THING (live) (*) b/w KANSAS CITY (live) (*)
(Vertigo GPS 1 (7"), 10/1976, UK)
Available free with the first 5000 copies of "Heat Treatment," both tracks taken from "Live at Marble Arch."

HOTEL CHAMBERMAID b/w DON'T ASK ME QUESTIONS (live) (*)
(Vertigo 6059 158 (7"), 10/1976, UK)
Taken from "Live at Marble Arch." I got a copy of the New Musical Express from November 13th 1976, where this is (Tony Parsons) single of the week, "Heat Treatment" is album of the week, and the title story is about GP as well.

HEAT TREATMENT b/w BACK DOOR LOVE
(Mercury 73876 (7" & promo 7"), 1976, USA)

POURIN' IT ALL OUT b/w HELP ME SHAKE IT
(Vertigo 6059 161 (7"), 1/1977, UK)

PINK PARKER EP: HOLD BACK THE NIGHT (*) / (LET ME GET) SWEET ON YOU (*) b/w WHITE HONEY (live) (*) / SOUL SHOES (live) (*)
(Vertigo Park 001 (7"), 3/1977, UK)
(Mercury EP 74000 (7") and MK 28 (promo 12"), 3/1977, USA)

HOLD BACK THE NIGHT (*) b/w HOLD BACK THE NIGHT (*)
(Mercury DJ-491 (promo 7"), 1977, USA)

HOLD BACK THE NIGHT (*) b/w (LET ME GET) SWEET ON YOU (*)
(Vertigo DINK-001 (jukebox promo 7"), 1977, UK)
Live tracks again taken from "Live at Marble Arch." All four songs from the EP are included on the 2 CD compilation "Vertigo" from 1996.

NEW YORK SHUFFLE b/w THE BLEEP (**)
(Vertigo 6059 185 (7"), 11/1977, UK)
This is actually a "bleeped" version of "The Raid" from "Stick To Me." Although it's a different mix or take, this one's no must have.

STICK TO ME b/w ???
(Vertigo demo 7", UK)
Who knows more about this UK item?

STICK TO ME b/w HEAT IN HARLEM (edit, 4:12) (**)
(Mercury 73970 (7"), 1977, USA)

STICK TO ME b/w STICK TO ME
(Mercury DJ-531 (promo 7"), 1977, USA)
They edited out the second verse of "Heat In Harlem" and then faded much sooner at the end. It's the same take as on "Stick To Me."

HEY LORD, DON'T ASK ME QUESTIONS b/w WATCH THE MOON COME DOWN (live)
(Vertigo 6059 199 / Park 002 (7"), Park 12 (12"), and Jumbo 5 (promo 12"), 3/1978, UK)
"Hey Lord" is the studio version from "The Parkerilla." The B-side is the live version from "The Parkerilla," too.

MERCURY POISONING (*)
(One-sided Arista promo-12"; SP-41, 2/1979, USA)
Later available on many compilations and on the Razor & Tie reissue of "Another Grey Area."

PROTECTION b/w I WANT YOU BACK (ALIVE) (*)
(Vertigo 9198 101 (12") and 6059 219 (7"), 3/1979, UK)
Also available on the Razor & Tie reissue of "The Real Macaw" and many compilations. And despite the name this is the studio version. The only issued live version I know is on "Live Sparks."

DISCOVERING JAPAN b/w LOCAL GIRLS
(Vertigo 6059 226 (7"), 5/1979, UK)

LOCAL GIRLS b/w I WANT YOU BACK (ALIVE) (*)
(Arista AS 0420 (7"), 5/1979, USA, and Arista promo 12" SP-54, 1979, USA)

LOCAL GIRLS (mono) b/w LOCAL GIRLS (stereo)
(Arista promo 7" AS 0420, 1979, USA)

I WANT YOU BACK (ALIVE) (*) b/w MERCURY POISONING (*)
(Arista AS 0439 (7" & promo 7"), 1979, USA)
The cover of the former 7"-single says only "I Want You Back," just as the Jackson Five original was called. The latter single was (only?) available free by sending the catalog number from the back of the US-issue of "Squeezing Out Sparks" to Arista.

STUPEFACTION b/w WOMEN IN CHARGE (**)
(Stiff BUY 72 (7"), 4/1980, UK)
(Arista AS 0523 (7"), 1980, USA)

STUPEFACTION b/w PARALYSED
(Stiff BUY 72 (7"), 1980, UK)
"Women In Charge" is now available in a completely different mix on the Razor & Tie reissue of "Up Escalator." In the UK it was also an extra track on the tape version of "Up Escalator" on Stiff Records in 1980. And "Stupefaction" really was released with two different B-sides under the same number (Stiff BUY 72) in the UK.

LOVE WITHOUT GREED b/w MERCURY POISONING (live) (*)
(Stiff BUY 82 (7"), 6/27/1980, UK)
Taken from "Live Sparks," now available on the Stiff box set from Demon/Rhino and on the new "A Hard Nights Day" Stiff compilation from MCA UK.

ENDLESS NIGHT b/w NO HOLDING BACK
(Arista AS 0549 (7" & promo 7"), 1980, USA)

DISCOGRAPHY: Graham Parker albums

LIVE AT MARBLE ARCH
(Vertigo promo album, 7/1976, UK)
Produced by Nick Lowe
Side 1: White Honey / That's What They All Say / Back Door Love / Back to Schooldays / Silly Thing
Side 2: Chain of Fools / Don't Ask Me Questions / You Can't Hurry Love / Soul Shoes / Kansas City
All tracks have been issued officially in 1996 on the "Vertigo" compilation double CD.

HEAT TREATMENT
(Vertigo 10/1976, UK)
(Mercury 10/1976, USA)
Produced by Robert John Lange and (*) Nick Lowe
Engineered by Robert John Lange, Dave Charles & Pete Kelsey
Recorded at Rockfield Studios, Monmouth, South Wales
Mixed at Trident Studios, St Anne's Court, London
Side 1: Heat Treatment / That's What They All Say / Turned Up Too Late / Black Honey / Hotel Chambermaid
Side 2: Pourin' It All Out / Back Door Love (*) / Something You're Going Through / Help Me Shake It / Fools' Gold

STICK TO ME
(Vertigo 10/1977, UK)
(Mercury 10/1977, USA)
Produced by Nick Lowe
Executive producers Dave Robinson & Jake Riviera
Engineered by Roger Bechirian
Recorded and mixed at Eden Studios, Chiswick, London
Side 1: Stick To Me / I'm Gonna Tear Your Playhouse Down / Problem Child / Soul On Ice / Clear Head
Side 2: The New York Shuffle / Watch The Moon Come Down / Thunder And Rain / The Heat In Harlem / The Raid

THE PARKERILLA
(Vertigo 5/1978, UK)
(Mercury 5/1978, USA)
Sides 1 - 3: Recording mixed by Robert John Lange, Musical Director Bob Andrews
Side 4: Produced by Robert John Lange
Recorded at Bournemouth Winter Gardens, Manchester Palace, Oxford New Theatre, New York Palladium
Side 1: Lady Doctor / Fool's Gold / Tear Your Playhouse Down / Hey Lord, Don't Ask Me Questions (all tracks live)
Side 2: The Heat In Harlem / Silly Thing / Gypsy Blood / Back To School Days (all tracks live)
Side 3: Heat Treatment / Watch The Moon Come Down / New York Shuffle / Soul Shoes (all tracks live)
Side 4: Hey Lord, Don't Ask Me Questions (alternate studio recording)

SQUEEZING OUT SPARKS
(Vertigo 3/1979, UK)
(Arista 3/1979, USA)
Produced by Jack Nitzsche
Engineered by Mark Howlett
Recorded at Lansdowne Studios, London
Mixed at Cherokee Studios, Hollywood
Side 1: Discovering Japan / Local Girls / Nobody Hurts You / You Can't Be Too Strong / Passion Is No Ordinary Word
Side 2: Saturday Nite Is Dead / Love Gets You Twisted / Protection / Waiting For The UFOs / Don't Get Excited

LIVE SPARKS
(Vertigo promo album, 1979, UK)
(Arista promo album SP63, 1979, USA)
Mixed and awakened by Ron Wolfe
Side 1: Discovering Japan / Local Girls / Nobody Hurts You / You Can't Be Too Strong / Passion Is No Ordinary Word / I Want You Back (Alive)
Side 2: Saturday Nite Is Dead / Love Gets You Twisted / Protection / Waiting For The UFOs / Don't Get Excited / Mercury Poisoning
This album was compiled from two 1979 radio shows from San Francisco and Chicago. First time officially released 10/1/1996 by Arista in the USA on one CD together with "Squeezing Out Sparks." The two non-SOS songs ("I Want You Back (Alive)" and "Mercury Poisoning") were relegated to the end of the CD.

THE UP ESCALATOR
(Stiff 4/1980, UK)
Produced by Jimmy Iovine
Engineered by Shelly Yakus
Side 1: No Holding Back / Devil's Sidewalk / Stupefaction / Love Without Greed / Jolie Jolie
Side 2: Endless Night / Paralyzed / Maneuvers / Empty Lives / The Beating Of Another Heart