diff --git a/pkg/kubelet/cm/cpumanager/BUILD b/pkg/kubelet/cm/cpumanager/BUILD
index e44b07bc8a2..6236164c799 100644
--- a/pkg/kubelet/cm/cpumanager/BUILD
+++ b/pkg/kubelet/cm/cpumanager/BUILD
@@ -3,6 +3,7 @@ load("@io_bazel_rules_go//go:def.bzl", "go_library", "go_test")
 go_library(
     name = "go_default_library",
     srcs = [
+        "container_map.go",
         "cpu_assignment.go",
         "cpu_manager.go",
         "fake_cpu_manager.go",
diff --git a/pkg/kubelet/cm/cpumanager/container_map.go b/pkg/kubelet/cm/cpumanager/container_map.go
new file mode 100644
index 00000000000..2da2c931b60
--- /dev/null
+++ b/pkg/kubelet/cm/cpumanager/container_map.go
@@ -0,0 +1,68 @@
+/*
+Copyright 2019 The Kubernetes Authors.
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+    http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*/
+
+package cpumanager
+
+import (
+	"fmt"
+
+	"k8s.io/api/core/v1"
+)
+
+// containerMap maps (podUID, containerName) -> containerID
+type containerMap map[string]map[string]string
+
+func newContainerMap() containerMap {
+	return make(containerMap)
+}
+
+func (cm containerMap) Add(p *v1.Pod, c *v1.Container, containerID string) {
+	podUID := string(p.UID)
+	if _, exists := cm[podUID]; !exists {
+		cm[podUID] = make(map[string]string)
+	}
+	cm[podUID][c.Name] = containerID
+}
+
+func (cm containerMap) Remove(containerID string) {
+	found := false
+	for podUID := range cm {
+		for containerName := range cm[podUID] {
+			if containerID == cm[podUID][containerName] {
+				delete(cm[podUID], containerName)
+				found = true
+				break
+			}
+		}
+		if len(cm[podUID]) == 0 {
+			delete(cm, podUID)
+		}
+		if found {
+			break
+		}
+	}
+}
+
+func (cm containerMap) Get(p *v1.Pod, c *v1.Container) (string, error) {
+	podUID := string(p.UID)
+	if _, exists := cm[podUID]; !exists {
+		return "", fmt.Errorf("pod %s not in containerMap", podUID)
+	}
+	if _, exists := cm[podUID][c.Name]; !exists {
+		return "", fmt.Errorf("container %s not in containerMap for pod %s", c.Name, podUID)
+	}
+	return cm[podUID][c.Name], nil
+}
diff --git a/pkg/kubelet/cm/cpumanager/policy_static.go b/pkg/kubelet/cm/cpumanager/policy_static.go
index 38dce8b08e3..c374cb42e55 100644
--- a/pkg/kubelet/cm/cpumanager/policy_static.go
+++ b/pkg/kubelet/cm/cpumanager/policy_static.go
@@ -73,6 +73,10 @@ type staticPolicy struct {
 	topology *topology.CPUTopology
 	// set of CPUs that is not available for exclusive assignment
 	reserved cpuset.CPUSet
+	// containerMap provides a mapping from
+	// (pod, container) -> containerID
+	// for all containers a pod
+	containerMap containerMap
 }
 
 // Ensure staticPolicy implements Policy interface
@@ -97,8 +101,9 @@ func NewStaticPolicy(topology *topology.CPUTopology, numReservedCPUs int) Policy
 	klog.Infof("[cpumanager] reserved %d CPUs (\"%s\") not available for exclusive assignment", reserved.Size(), reserved)
 
 	return &staticPolicy{
-		topology: topology,
-		reserved: reserved,
+		topology:     topology,
+		reserved:     reserved,
+		containerMap: newContainerMap(),
 	}
 }
 
@@ -172,7 +177,15 @@ func (p *staticPolicy) assignableCPUs(s state.State) cpuset.CPUSet {
 	return s.GetDefaultCPUSet().Difference(p.reserved)
 }
 
-func (p *staticPolicy) AddContainer(s state.State, pod *v1.Pod, container *v1.Container, containerID string) error {
+func (p *staticPolicy) AddContainer(s state.State, pod *v1.Pod, container *v1.Container, containerID string) (rerr error) {
+	// So long as this function does not return an error,
+	// add (pod, container, containerID) to the containerMap.
+	defer func() {
+		if rerr == nil {
+			p.containerMap.Add(pod, container, containerID)
+		}
+	}()
+
 	if numCPUs := guaranteedCPUs(pod, container); numCPUs != 0 {
 		klog.Infof("[cpumanager] static policy: AddContainer (pod: %s, container: %s, container id: %s)", pod.Name, container.Name, containerID)
 		// container belongs in an exclusively allocated pool
@@ -182,6 +195,22 @@ func (p *staticPolicy) AddContainer(s state.State, pod *v1.Pod, container *v1.Co
 			return nil
 		}
 
+		// Proactively remove CPUs from init containers that have already run.
+		// They are guaranteed to have run to completion before any other
+		// container is run.
+		for _, initContainer := range pod.Spec.InitContainers {
+			if container.Name != initContainer.Name {
+				initContainerID, err := p.containerMap.Get(pod, &initContainer)
+				if err != nil {
+					continue
+				}
+				err = p.RemoveContainer(s, initContainerID)
+				if err != nil {
+					klog.Warningf("[cpumanager] unable to remove init container (container id: %s, error: %v)", initContainerID, err)
+				}
+			}
+		}
+
 		cpuset, err := p.allocateCPUs(s, numCPUs)
 		if err != nil {
 			klog.Errorf("[cpumanager] unable to allocate %d CPUs (container id: %s, error: %v)", numCPUs, containerID, err)
@@ -193,7 +222,15 @@ func (p *staticPolicy) AddContainer(s state.State, pod *v1.Pod, container *v1.Co
 	return nil
 }
 
-func (p *staticPolicy) RemoveContainer(s state.State, containerID string) error {
+func (p *staticPolicy) RemoveContainer(s state.State, containerID string) (rerr error) {
+	// So long as this function does not return an error,
+	// remove containerID from the containerMap.
+	defer func() {
+		if rerr == nil {
+			p.containerMap.Remove(containerID)
+		}
+	}()
+
 	klog.Infof("[cpumanager] static policy: RemoveContainer (container id: %s)", containerID)
 	if toRelease, ok := s.GetCPUSet(containerID); ok {
 		s.Delete(containerID)