Tell Tomcat to drop requests instead of dying "All threads (150) are currently busy"

My Tomcat 6.0.26 sometimes dies saying:

SEVERE: All threads (150) are currently busy, waiting. Increase maxThreads (150) or check the servlet status

... then Tomcat shuts down, and users can't access the webapp until I restart Tomcat manually.

Some of the threads indeed take a long time to execute, it is by-design, not a thread-gone-wild problem.

I know I could increase maxThreads, but that is not a viable solution, because the server might receive requests even more requests.

QUESTION: Instead of dying, can I tell Tomcat to just drop requests when maxThreads is reached and the AJP/1.3 backlog is full?

Below is my server.xml in any case:

<?xml version='1.0' encoding='utf-8'?>
<Server port="8005" shutdown="SHUTDOWN">
  <Listener className="org.apache.catalina.core.AprLifecycleListener" SSLEngine="on" />
  <Listener className="org.apache.catalina.core.JasperListener" />
  <Listener className="org.apache.catalina.mbeans.ServerLifecycleListener" />
  <Listener className="org.apache.catalina.mbeans.GlobalResourcesLifecycleListener" />
  <GlobalNamingResources>
    <Resource name="UserDatabase" auth="Container"
              type="org.apache.catalina.UserDatabase"
              description="User database that can be updated and saved"
              factory="org.apache.catalina.users.MemoryUserDatabaseFactory"
              pathname="conf/tomcat-users.xml" />
  </GlobalNamingResources>
  <Service name="Catalina">
    <Executor name="tomcatThreadPool" namePrefix="catalina-exec-" minSpareThreads="100"/>
    <Connector port="8080" protocol="HTTP/1.1"
               connectionTimeout="20000"
               redirectPort="8443" />
    <Connector port="8009" protocol="AJP/1.3" redirectPort="8443"
               enableLookups="false" useBodyEncodingForURI="true"
               backlog="150" maxThreads="150" executor="tomcatThreadPool"
               keepAliveTimeout="5000" connectionTimeout="300000" />
    <Engine name="Catalina" defaultHost="localhost" jvmRoute="ecm1">
      <Realm className="org.apache.catalina.realm.UserDatabaseRealm"
             resourceName="UserDatabase"/>
      <Host name="localhost"  appBase="webapps"
            unpackWARs="true" autoDeploy="true"
            xmlValidation="false" xmlNamespaceAware="false">
      </Host>
    </Engine>
  </Service>
</Server>