How can I set a default shipping fee on my online store?

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Hello and good morning.

Is there a way to set a default shipping fee and then have a secondary shipping fee?

Here's my scenario; I have 2 shipping fees associated with my store. Your first order carries a flat rate $6 shipping charge. If you please another order before your first order ships, you only have to pay $1. I have both shipping fees set up in my shipping profile but when you go to check out, the $1 fee shows up first and I've had customers use that before using the $6 fee. How can I make to where the $6 fee is the default shipping fee and then to get to the $1 fee, they need to use the shipping drop down menu?

OR is there a way to offer a discount code? I know I can offer a code for free shipping but what about discounted shipping? The site limits you on how you can use discount codes so I don't want to lose other discounts I have setup...

Thanks in advance for your help!