How to update multiple components (selectOneMenu) with depending objects relations?

i have the following (self-explanatory) entity-relation:

* Manufacturer
* Car    (Manufacturer.getCars())
* Tire   (Car.getTires())

MyBean

private List<Manufacturer> allManufacturers

private Manufacturer selectedManufacturer
private Car selectedCar
private Tire selectedTire

xhtml

<p:selectOneMenu id="manufacturerSel" value="#{myBean.selectedManufacturer}" converter="#{manufacturerConverter}">
    <f:selectItem itemLabel="None" itemValue="#{null}" />
    <f:selectItems value="#{myBean.allManufacturers}" />
    <p:ajax update="carSel tireSel" />
</p:selectOneMenu>

<p:selectOneMenu id="carSel" value="#{myBean.selectedCar}" converter="#{carsConverter}" disabled="#{empty myBean.selectedManufacturer.cars}">
    <f:selectItem itemLabel="None" itemValue="#{null}" />
    <f:selectItems value="#{myBean.selectedManufacturer.cars}"  />
    <p:ajax update="tireSel" />
</p:selectOneMenu>

<p:selectOneMenu id="tireSel" value="#{myBean.selectedTire}" converter="#{tiresConverter}" disabled="#{empty myBean.selectedCar.tires}">
    <f:selectItem itemLabel="None" itemValue="#{null}" />                            
    <f:selectItems value="#{myBean.selectedCars.tires}"  />
</p:selectOneMenu>

• the last two p:selectOneMenu should be updated depending on the selection in the first one
• The last p:selectOneMenu with ID tireSel is not being updated correctly
• All the to-be-updated components are inside the same NamingContainer
• the carSel gets updated, but the values loaded in tireSel are strange (seem to be valid for the last request)
• i also tried update="@form" in manufacturerSel

EDIT To show which EL Version is used: Here´s an excerpt of my pom.xml

<dependency>
    <groupId>javax.faces</groupId>
    <artifactId>javax.faces-api</artifactId>
    <version>2.1</version>
</dependency>
<dependency>
    <groupId>org.glassfish</groupId>
    <artifactId>javax.faces</artifactId>
    <version>2.1.12</version>
</dependency>    
<dependency>
    <groupId>javax.el</groupId>
    <artifactId>el-api</artifactId>
    <version>2.2</version>
    <scope>provided</scope>
</dependency>

You basically need to clear out the selectedCar value. You can use <p:ajax listener> for this.

<p:ajax listener="#{myBean.clearSelectedCar}" update="carSel tireSel" />

with

public void clearSelectedCar() {
    selectedCar = null; // You might want to clear selectedTire as well.
}

Otherwise the old selected value will still retain in the bean and the list of tires will still depend on that.