diff --git a/src/core/chunked_stream.js b/src/core/chunked_stream.js
index 39c1cb677..a0f29ec74 100644
--- a/src/core/chunked_stream.js
+++ b/src/core/chunked_stream.js
@@ -159,7 +159,9 @@ class ChunkedStream {
     if (pos >= this.end) {
       return -1;
     }
-    this.ensureByte(pos);
+    if (pos >= this.progressiveDataLength) {
+      this.ensureByte(pos);
+    }
     return this.bytes[this.pos++];
   }
 
@@ -187,7 +189,9 @@ class ChunkedStream {
     const strEnd = this.end;
 
     if (!length) {
-      this.ensureRange(pos, strEnd);
+      if (strEnd > this.progressiveDataLength) {
+        this.ensureRange(pos, strEnd);
+      }
       const subarray = bytes.subarray(pos, strEnd);
       // `this.bytes` is always a `Uint8Array` here.
       return (forceClamped ? new Uint8ClampedArray(subarray) : subarray);
@@ -197,7 +201,9 @@ class ChunkedStream {
     if (end > strEnd) {
       end = strEnd;
     }
-    this.ensureRange(pos, end);
+    if (end > this.progressiveDataLength) {
+      this.ensureRange(pos, end);
+    }
 
     this.pos = end;
     const subarray = bytes.subarray(pos, end);
@@ -224,7 +230,9 @@ class ChunkedStream {
     if (end > this.end) {
       end = this.end;
     }
-    this.ensureRange(begin, end);
+    if (end > this.progressiveDataLength) {
+      this.ensureRange(begin, end);
+    }
     return this.bytes.subarray(begin, end);
   }
 
@@ -245,7 +253,9 @@ class ChunkedStream {
 
   makeSubStream(start, length, dict) {
     if (length) {
-      this.ensureRange(start, start + length);
+      if (start + length > this.progressiveDataLength) {
+        this.ensureRange(start, start + length);
+      }
     } else {
       // When the `length` is undefined you do *not*, under any circumstances,
       // want to fallback on calling `this.ensureRange(start, this.end)` since
@@ -256,7 +266,9 @@ class ChunkedStream {
       // time/resources during e.g. parsing, since `MissingDataException`s will
       // require data to be re-parsed, which we attempt to minimize by at least
       // checking that the *beginning* of the data is available here.
-      this.ensureByte(start);
+      if (start >= this.progressiveDataLength) {
+        this.ensureByte(start);
+      }
     }
 
     function ChunkedStreamSubstream() {}