Possible Clues:

• Not a fat pair, by the sound of it, that gets shed
• Roof type
• Working alone, having time in shed
• That's inclined to be shed
• Rested on empty shed
• No fat to be shed
• Incline in the direction of building
• Shed a little off the perpendicular?
• Small building resting on side of larger one
• Shed the skinny pair, by the sound of it