Rain diverter for rubber membrane roof?

There's a small roof (about 6' wide by 4' deep) above my front door. Rain and melting snow run off the front of the roof onto the stairs, making them icy in the winter.
We got one estimate for about $600, because the contractor says we'd have to rebuild the entire roof to change its slope. It currently is a hip roof, and I think he wants to rebuild it to slope entirely to the sides instead of to the front.
I'd prefer to just install a rain diverter strip. The websites that describe them all show shingle roofs, but ours is a rubber membrane roof with copper flashing at the edge. Is a rain diverter an option?
Jimmy
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snipped-for-privacy@mailinator.com wrote:

This may sound like a dumb question, but why not a gutter? Maybe something like copper, since it's at the front of the house and therefore probably noticeable?
nate
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...
That would be another option, but I thought it would be overkill for a roof this small. There would also be the aesthetic issue of running the downspout down the narrow wooden post holding up the roof.
Other similar (19th century) houses on my street don't have gutters on their porch roofs. I'm not sure what they do have -- it's tough to see a diverter from the ground.
Jimmy
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wrote:

You do not have to use a downspout. Just let the gutter dump the water to the side like a rooftop diverter would.
Don Young
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snipped-for-privacy@mailinator.com wrote in wrote:

How about a nice bead of caulk along the edge to guide the water away?
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Best regards
Han
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