In this study, patients with wake-up stroke will be randomized to thrombolysis with tenecteplase and best standard treatment or to best standard treatment without thrombolysis. Tenecteplase has several potential advantages over alteplase, including very rapid action and that it can be given as a single injection. Prior to thrombolysis, a brain scan must be done to exclude bleeding or significant brain damage as a result from the stroke. We will use a CT scan to inform this decision. CT is used as a routine examination in all stroke patients. Other studies testing clot-busting treatment in wake-up stroke are using alteplase and more complex brain scans, which are not routinely available in the emergency situation in all hospitals.