See the definition of peplum below.

Sweet Pea Navy Mesh Knotted Blouson Top - Bluefly.com
Sweet Pea tops are un-boring basics to keep you in a flirty state of mind. • Color: Navy • Mesh nylon knit • High, knotted keyhole front and back neck • Gathered detail along shoulder straps • Elasticized waist with **raw-edged, peplum hem** • 100% Nylon; Hand Wash; Imported; style #2082048
http://teamsugar.com/541946

Peplum - A short overskirt or ruffle attached at the waistline of a jacket, blouse, dress or skirt.
Peplum - Short flounce attached to a snugly fitting waistline.
Peplum - A separate section between the waist and hipline, usually on a jacket. Section can be pleated or gathered to create flare.
http://www.mycustomtailor.com/glossary.php

À la basque – shirt tail
http://www.proz.com/kudoz/2619050




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Note added at 1 hr (2008-05-27 15:20:48 GMT)
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Well, I think that I could have written the language variant entry better ;-) , especially since I left blouse out. Blouse with unfinished ruffled hem [or edges] would have been a better entry. Anyway, here are more examples for variations.

Angelic powder pink silk chiffon gown has very fine, soft, and sheer white organza fabric which make up the flounce sleeves and neckline accents. The trimming has **unfinished edges**, which are slightly frayed, and the effect is almost like floating flowers.
http://www.vintage-hollywood.com/product_info.php?products_i...

Stretch silk blouse is styled with a Mandarin collar, **unfinished hem and ruffles** around the placket, bib and cuffs.
http://shop.nordstrom.com/S/2887253?cm_ven=yahoo&cm_cat=data...

Scoop v-neck. **Unfinished ruffled hem** at sleeves. Bird and rose design with rhinestones. Signature Ed Hardy(R) logo on back. 100% cotton. Machine wash. Lay flat to dry.
http://www.fashionbeauti.com/Back-To-School-Give-Me-A-Decent...

MISSES’ JACKET AND DRESS: Fitted, lined jacket has princess seams with topstitch trim and single layer **flounce (wrong side of fabric shows) with unfinished edges** [see schema]
http://www.voguepatterns.com/item/V8283.htm?&next=1

FULL TILT Matilda Womens Tube
Full Tilt Matilda knit tube top with empire waistline. Thick, elastic band around top holds securely. Elastic waistline has a thick braided drawstring that ties in front. **Ruffled flounce with unfinished hem**. 47% rayon/47% polyester/6% spandex. Hand wash. Made in USA.
http://www.tillys.com/tillys/variants.aspx?prod=134733700&ct...

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Note added at 7 hrs (2008-05-27 21:48:23 GMT)
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In the definition that you give for basque, the peplum is the short skirt which is attached to a blouse or jacket with a fitted waist. And the Lexique textile gives peplum as a translation for "basque."

Recently, I did some research on peplums and "basques" for a question on split waists. I'm going to include some of the links to the garments I used as examples. Note how one of these jackets has a slightly flared peplum and another has a frilly, gathered peplum.

My personal preference is to use peplum since it is actually used quite a bit in advertising.

basquenf (vêt. masc.) – tail, skirt
basque (vêt. fem.) – peplum, lap
Lexique textile de Pierre Hirsch

basque ( d’un vêtement ) Partie rapportée d’une veste qui part de la taille et descend plus ou moins bas sur les hanches. Partie découpée d’une jaquette, d’un habit de cérémonie ou d’une veste qui descend plus bas que la taille. tail The back, last , lower, or inferior part of something.
http://www.textiles-mtl.com/French/glossary/f_glossary_B_fra...

Couronne dorée, cheveux noirs crêpés, manteau mauve bordé d'une bande mauve, jaune et blanche (couleurs de la ville), blouse blanche avec ceinture mauve, aigles bicéphales mauves sur **la basque de la blouse**, soutien-gorge argenté avec représentation des armes de la ville, sceptre et couronne dans la main droite cerclant un plat jaune doré avec, peintes en noir, les armes de la ville, la jupe est jaune avec en dessous, un jupon blanc. [see picture]
http://fr.wikipedia.org/wiki/Mlle_Victoire

[from the split waist question]
[frilly, gathered peplum]
3| Douceur chromatique du vison gris avec une veste au drapé péplum très sobre en accord avec une robe en satin 1940 – ROBERTO CAVALLI.
http://www.fur-style.com/fr/forecasts/modern-sport/catwalk/

[smooth, flared peplum]
en 100% lin chiné. Finitions point sellier contrastant. Profond col tailleur. Gros bouton. Poignets à revers. Découpes princesse devant et dos. **Basque devant et dos. Découpe milieu dos.** Doublure 100% polyester. Long. 62 cm.
http://www.daxon.fr/veste-femme/rwp/p-0001003585073w4g.aspx

La veste ANNE WEYBURN. Tissu uni 100 % polyester légèrement satiné à effet flammé. Doublure taffetas polyester. Infroissable et lavable en machine. Légèrement appuyée par découpes princesse devant et dos. Col officier, **découpe taille formant basque.** Poignets jacquard fendus. Long. 62 cm.
http://www.laredoute.fr/product.aspx?productid=324113985&doc...

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Note added at 7 hrs (2008-05-27 21:52:07 GMT)
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Also, if you don't want to use peplum, consider using flounce. Compare the flounce at the Vogue pattern site with the garments with a peplum.

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Note added at 2 days2 hrs (2008-05-29 16:09:40 GMT) Post-grading
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You're welcome, Philipa, and thank you. And I'm always happy to be called Claire. My high school French teacher gave us all French names and I've been called Claire ever since :-)