diff --git a/library/src/main/java/com/google/android/exoplayer2/upstream/AssetDataSource.java b/library/src/main/java/com/google/android/exoplayer2/upstream/AssetDataSource.java
index ff7ea42d4d7..1a685ca1af0 100644
--- a/library/src/main/java/com/google/android/exoplayer2/upstream/AssetDataSource.java
+++ b/library/src/main/java/com/google/android/exoplayer2/upstream/AssetDataSource.java
@@ -137,18 +137,18 @@ public Uri getUri() {
   @Override
   public void close() throws AssetDataSourceException {
     uri = null;
-    if (inputStream != null) {
-      try {
+    try {
+      if (inputStream != null) {
         inputStream.close();
-      } catch (IOException e) {
-        throw new AssetDataSourceException(e);
-      } finally {
-        inputStream = null;
-        if (opened) {
-          opened = false;
-          if (listener != null) {
-            listener.onTransferEnd(this);
-          }
+      }
+    } catch (IOException e) {
+      throw new AssetDataSourceException(e);
+    } finally {
+      inputStream = null;
+      if (opened) {
+        opened = false;
+        if (listener != null) {
+          listener.onTransferEnd(this);
         }
       }
     }
diff --git a/library/src/main/java/com/google/android/exoplayer2/upstream/ContentDataSource.java b/library/src/main/java/com/google/android/exoplayer2/upstream/ContentDataSource.java
index 838a7970dc3..2a0ad014897 100644
--- a/library/src/main/java/com/google/android/exoplayer2/upstream/ContentDataSource.java
+++ b/library/src/main/java/com/google/android/exoplayer2/upstream/ContentDataSource.java
@@ -45,6 +45,7 @@ public ContentDataSourceException(IOException cause) {
   private final TransferListener<? super ContentDataSource> listener;
 
   private Uri uri;
+  private AssetFileDescriptor assetFileDescriptor;
   private InputStream inputStream;
   private long bytesRemaining;
   private boolean opened;
@@ -69,8 +70,8 @@ public ContentDataSource(Context context, TransferListener<? super ContentDataSo
   public long open(DataSpec dataSpec) throws ContentDataSourceException {
     try {
       uri = dataSpec.uri;
-      AssetFileDescriptor assetFd = resolver.openAssetFileDescriptor(uri, "r");
-      inputStream = new FileInputStream(assetFd.getFileDescriptor());
+      assetFileDescriptor = resolver.openAssetFileDescriptor(uri, "r");
+      inputStream = new FileInputStream(assetFileDescriptor.getFileDescriptor());
       long skipped = inputStream.skip(dataSpec.position);
       if (skipped < dataSpec.position) {
         // We expect the skip to be satisfied in full. If it isn't then we're probably trying to
@@ -135,13 +136,22 @@ public Uri getUri() {
   @Override
   public void close() throws ContentDataSourceException {
     uri = null;
-    if (inputStream != null) {
-      try {
+    try {
+      if (inputStream != null) {
         inputStream.close();
+      }
+    } catch (IOException e) {
+      throw new ContentDataSourceException(e);
+    } finally {
+      inputStream = null;
+      try {
+        if (assetFileDescriptor != null) {
+          assetFileDescriptor.close();
+        }
       } catch (IOException e) {
         throw new ContentDataSourceException(e);
       } finally {
-        inputStream = null;
+        assetFileDescriptor = null;
         if (opened) {
           opened = false;
           if (listener != null) {
diff --git a/library/src/main/java/com/google/android/exoplayer2/upstream/FileDataSource.java b/library/src/main/java/com/google/android/exoplayer2/upstream/FileDataSource.java
index bed018d76c6..d211cfacbd3 100644
--- a/library/src/main/java/com/google/android/exoplayer2/upstream/FileDataSource.java
+++ b/library/src/main/java/com/google/android/exoplayer2/upstream/FileDataSource.java
@@ -109,18 +109,18 @@ public Uri getUri() {
   @Override
   public void close() throws FileDataSourceException {
     uri = null;
-    if (file != null) {
-      try {
+    try {
+      if (file != null) {
         file.close();
-      } catch (IOException e) {
-        throw new FileDataSourceException(e);
-      } finally {
-        file = null;
-        if (opened) {
-          opened = false;
-          if (listener != null) {
-            listener.onTransferEnd(this);
-          }
+      }
+    } catch (IOException e) {
+      throw new FileDataSourceException(e);
+    } finally {
+      file = null;
+      if (opened) {
+        opened = false;
+        if (listener != null) {
+          listener.onTransferEnd(this);
         }
       }
     }