Use max-height in the transition and not height. And set a value on max-height to something bigger than your box will ever get.

See JSFiddle demo provided by Chris Jordan in another answer here.

#menu #list {
    max-height: 0;
    transition: max-height 0.15s ease-out;
    overflow: hidden;
    background: #d5d5d5;
}

#menu:hover #list {
    max-height: 500px;
    transition: max-height 0.25s ease-in;
}

<div id="menu">
    <a>hover me</a>
    <ul id="list">
        <!-- Create a bunch, or not a bunch, of li's to see the timing. -->
        <li>item</li>
        <li>item</li>
        <li>item</li>
        <li>item</li>
        <li>item</li>
    </ul>
</div>