diff --git a/src/workerd/api/streams/internal.c++ b/src/workerd/api/streams/internal.c++
index 94b3d94d2df..5d25d0e63a2 100644
--- a/src/workerd/api/streams/internal.c++
+++ b/src/workerd/api/streams/internal.c++
@@ -48,6 +48,8 @@ kj::Promise<void> pumpTo(ReadableStreamSource& input, WritableStreamSink& output
 class AllReader {
   // Modified from AllReader in kj/async-io.c++.
 
+  using PartList = kj::Array<kj::ArrayPtr<byte>>;
+
 public:
   explicit AllReader(ReadableStreamSource& input, uint64_t limit)
       : input(input), limit(limit) {
@@ -59,58 +61,53 @@ public:
   }
 
   kj::Promise<kj::Array<byte>> readAllBytes() {
-    auto parts = co_await readParts();
-    auto out = kj::heapArray<byte>(runningTotal);
-    copyInto(out, kj::mv(parts));
-    co_return out;
+    return loop().then([this](PartList&& partPtrs) {
+      auto out = kj::heapArray<byte>(runningTotal);
+      copyInto(out, kj::mv(partPtrs));
+      return kj::mv(out);
+    });
   }
 
   kj::Promise<kj::String> readAllText() {
-    auto parts = co_await readParts();
-    auto out = kj::heapArray<char>(runningTotal + 1);
-    copyInto(out.slice(0, out.size() - 1).asBytes(), kj::mv(parts));
-    out.back() = '\0';
-    co_return kj::String(kj::mv(out));
+    return loop().then([this](PartList&& partPtrs) {
+      auto out = kj::heapArray<char>(runningTotal + 1);
+      copyInto(out.slice(0, out.size() - 1).asBytes(), kj::mv(partPtrs));
+      out.back() = '\0';
+      return kj::String(kj::mv(out));
+    });
   }
 
 private:
   ReadableStreamSource& input;
   uint64_t limit;
+  kj::Vector<kj::Array<kj::byte>> parts;
   uint64_t runningTotal = 0;
 
-  struct Part {
-    kj::Array<byte> buffer;
-    size_t amount;
-  };
-  using PartList = kj::Vector<Part>;
-
-  kj::Promise<PartList> readParts() {
-    static constexpr size_t bufferSize = 4096;
-    PartList parts;
+  kj::Promise<PartList> loop() {
+    auto bytes = kj::heapArray<kj::byte>(4096);
 
-    while (true) {
-      auto buffer = kj::heapArray<kj::byte>(bufferSize);
-      auto amount = co_await input.tryRead(buffer.begin(), bufferSize, bufferSize);
-      runningTotal += amount;
-      JSG_REQUIRE(runningTotal < limit, TypeError, "Memory limit exceeded before EOF.");
-
-      if (amount > 0) {
-        Part part = { .buffer = kj::mv(buffer), .amount = amount };
-        parts.add(kj::mv(part));
+    return input.tryRead(bytes.begin(), 1, bytes.size())
+        .then([this, bytes = kj::mv(bytes)](size_t amount) mutable
+        -> kj::Promise<PartList> {
+      if (amount == 0) {
+        return KJ_MAP(p, parts) { return p.asPtr(); };
       }
 
-      if (amount < bufferSize) {
-        co_return kj::mv(parts);
+      runningTotal += amount;
+      if (runningTotal >= limit) {
+        return JSG_KJ_EXCEPTION(FAILED, TypeError, "Memory limit exceeded before EOF.");
       }
-    }
+      parts.add(bytes.slice(0, amount).attach(kj::mv(bytes)));
+      return loop();
+    });
   }
 
-  void copyInto(kj::ArrayPtr<byte> out, PartList&& in) {
+  void copyInto(kj::ArrayPtr<byte> out, PartList in) {
     size_t pos = 0;
     for (auto& part: in) {
-      KJ_ASSERT(part.amount <= out.size() - pos);
-      memcpy(out.begin() + pos, part.buffer.begin(), part.amount);
-      pos += part.amount;
+      KJ_ASSERT(part.size() <= out.size() - pos);
+      memcpy(out.begin() + pos, part.begin(), part.size());
+      pos += part.size();
     }
   }
 };