The present disclosure describes improved SELEX methods for producing aptamers that are capable of binding to target molecules and improved photoSELEX methods for producing photoreactive aptamers that are capable of both binding and covalently cross linking to target molecules. Specifically, the present disclosure describes methods for producing aptamers and photoaptamers having slower dissociation rate constants than are obtained using prior SELEX and photoSELEX methods. The disclosure further describes aptamers and photoaptamers having slower dissociation rate constants than those obtained using prior methods. In addition, the disclosure describes aptamer constructs that include a variety of functionalities, including a cleavable element, a detection element, and a capture or immobilization element.