As it's not possible to specify the invocation order in a @WebFilter, users are forced to explicitly specify <filter-mapping> in web.xml. This works in combination with a @WebFilter(filterName) in Glassfish and JBoss AS as follows:

@WebFilter(filterName="filter1")
public class Filter1 implements Filter {}

@WebFilter(filterName="filter2")
public class Filter2 implements Filter {}

with

<filter-mapping>
    <filter-name>filter1</filter-name>
    <url-pattern>/url1/*</url-pattern>
</filter-mapping>
<filter-mapping>
    <filter-name>filter2</filter-name>
    <url-pattern>/url2/*</url-pattern>
</filter-mapping>

However it fails in Tomcat 7.0.27 with the following confusing exception (the <url-pattern> *is* been set)

Caused by: java.lang.IllegalArgumentException: Filter mapping must specify either a <url-pattern> or a <servlet-name>
	at org.apache.catalina.core.StandardContext.validateFilterMap(StandardContext.java:3009)
	at org.apache.catalina.core.StandardContext.addFilterMap(StandardContext.java:2968)
	at org.apache.catalina.deploy.WebXml.configureContext(WebXml.java:1207)
	at org.apache.catalina.startup.ContextConfig.webConfig(ContextConfig.java:1294)
	at org.apache.catalina.startup.ContextConfig.configureStart(ContextConfig.java:855)
	at org.apache.catalina.startup.ContextConfig.lifecycleEvent(ContextConfig.java:345)
	at org.apache.catalina.util.LifecycleSupport.fireLifecycleEvent(LifecycleSupport.java:119)
	at org.apache.catalina.util.LifecycleBase.fireLifecycleEvent(LifecycleBase.java:90)
	at org.apache.catalina.core.StandardContext.startInternal(StandardContext.java:5161)
	at org.apache.catalina.util.LifecycleBase.start(LifecycleBase.java:150)
	... 7 more