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I have created a spiral using the "Add curve" function and want to taper just one end of it (kind of like extruding and narrowing). Is there a way to do this? If not, what would be the best way create a spiral that enables the modification of its ends. Thanks.

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You may do it using a curve as a Taper Object's target to change the thickness along the spiral's axis. You can then change its width using the curve's specials menu. enter image description here

After creating a curve add a Bezier Circle and set it as a target in the Bevel Object window (Curve Data header).
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Add a Bezier Curve and edit it in Edit Mode so it's straight and placed vertical. enter image description here

Select the spiral in Object Mode and set the newly added Bezier Curve as a Taper Object target. enter image description here

Modify the newly added curve to change the thickness along the spiral's axis. Experiment with it for different results. enter image description here enter image description here

Finally select the spiral in Object Mode, press W-->Width Size and drag the cursor away to change its width.
enter image description here

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Every curve point has a radius value that will adjust the bevel radius and can be found in the properties region.

curve point tranform properties

You can use ⎇ AltS to adjust the radius value and combined with proportional editing you can get a gradual falloff from the active point.

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