If you want to grow tall, say four to five feet high, try hyssop. Though it will block the view of anything behind it, you might have an area along the border which you will find applicable. I'm sure other members will be along shortly to give you suggestions of shorter perennials which may be more suitable to your wishes.

Hi, welcome to GoY, unless you can make your borders wider, you are going to be very restricted in your choice of perennials, they tend to spread out quite a bit, and would very soon outgrow a 10 inch border, Derek.

I agree with Derek. You would do better with annuals though this will put you to work in spring planting either seed or started. Your choice would be whatever is available to a suitable height and type for you at your local garden center.

Veronica austriaca is a nice perennial with blue spikes which remains pretty compact for a number of years. Penstemons too might be a possiblilty. But a 10" strip is unlikely ever to look very good with perennials as they will look out of proportion even if you find slim enough ones.. You didn't say whether the strip is bordered by a drive, house wall or lawn - if lawn you really need to sacrifice a strip and widen the bed.