In this paper, we show that Web protocols and technologies are good candidates to design the Internet of Things. This approach allows anyone to access embedded devices through a Web application, via a standard Web browser. This Web of Things requires to embed Web servers in hardware-constrained devices. We first analyze the traffics embedded Web servers have to handle. Starting from this analysis, we propose a new way to design embedded Web servers, using a dedicated TCP/IP stack and numerous cross-layer off-line pre-calculation (where information are shared between IP, TCP, HTTP and the Web application). We finally present a prototype -- named Smews -- as a proof of concept of our proposals. It has been embedded in tiny devices (smart cards, sensors and other embedded devices), with a requirement of only 200 bytes of RAM and 7 kilo-bytes of code. We show that it is significantly faster than other state of the art solutions. We made Smews source code publically available under an open-source license.