To remove both Discount and Estimated shipping you need to edit checkout.xml file which is located at /app/design/frontend/base/default/layout/checkout.xml
go to line no: 89
<block type="checkout/cart_coupon" name="checkout.cart.coupon" as="coupon" template="checkout/cart/coupon.phtml"/> <block type="checkout/cart_shipping" name="checkout.cart.shipping" as="shipping" template="checkout/cart/shipping.phtml"/> <block type="checkout/cart_crosssell" name="checkout.cart.crosssell" as="crosssell" template="checkout/cart/crosssell.phtml"/>
comment out the highlighted portion like this
<!-- <block type="checkout/cart_coupon" name="checkout.cart.coupon" as="coupon" template="checkout/cart/coupon.phtml"/> <block type="checkout/cart_shipping" name="checkout.cart.shipping" as="shipping" template="checkout/cart/shipping.phtml"/> -->
you are done. If still both the blocks appear clear cache. So finally your checkout page will look like this.
http://magento-losung.blogspot.com/2013/01/remove-discount-and-estimated-shipping.html