diff --git a/Sources/NIOHTTP2/NGHTTP2Session.swift b/Sources/NIOHTTP2/NGHTTP2Session.swift
index 6019e998..2c7a7d1c 100644
--- a/Sources/NIOHTTP2/NGHTTP2Session.swift
+++ b/Sources/NIOHTTP2/NGHTTP2Session.swift
@@ -284,9 +284,22 @@ fileprivate struct StreamManager {
 
     // Discard old and unnecessary streams.
     private mutating func purgeOldStreams() {
-        while self.streamMap.count >= maxSize {
-            let lowestStreamID = self.streamMap.filter { !$0.value.active }.keys.sorted().first { $0 != 0 && $0 != Int32.max }!
-            self.streamMap.removeValue(forKey: lowestStreamID)
+        // If the stream map is not full, we don't purge.
+        guard self.streamMap.count >= self.maxSize else { return }
+
+        // It's full, time to purge some entries.
+        var purgeableStreamIDIterator = self.streamMap.lazy.filter { entry in
+            if entry.key == 0 || entry.key == Int32.max {
+                // Exclude the streams with max or min stream IDs.
+                return false
+            }
+
+            // We only want inactive streams.
+            return !entry.value.active
+        }.map { $0.key }.sorted().makeIterator()
+
+        while self.streamMap.count >= maxSize, let toPurge = purgeableStreamIDIterator.next() {
+            self.streamMap.removeValue(forKey: toPurge)
         }
     }
 }
diff --git a/Tests/NIOHTTP2Tests/SimpleClientServerTests+XCTest.swift b/Tests/NIOHTTP2Tests/SimpleClientServerTests+XCTest.swift
index 2b8f7b20..e2717e81 100644
--- a/Tests/NIOHTTP2Tests/SimpleClientServerTests+XCTest.swift
+++ b/Tests/NIOHTTP2Tests/SimpleClientServerTests+XCTest.swift
@@ -57,6 +57,7 @@ extension SimpleClientServerTests {
                 ("testStreamCloseEventForGoawayFiresAfterFrame", testStreamCloseEventForGoawayFiresAfterFrame),
                 ("testManyConcurrentInactiveStreams", testManyConcurrentInactiveStreams),
                 ("testDontRemoveActiveStreams", testDontRemoveActiveStreams),
+                ("testCachingInteractionWithMaxConcurrentStreams", testCachingInteractionWithMaxConcurrentStreams),
            ]
    }
 }
diff --git a/Tests/NIOHTTP2Tests/SimpleClientServerTests.swift b/Tests/NIOHTTP2Tests/SimpleClientServerTests.swift
index f4ba9475..3dc239c3 100644
--- a/Tests/NIOHTTP2Tests/SimpleClientServerTests.swift
+++ b/Tests/NIOHTTP2Tests/SimpleClientServerTests.swift
@@ -1317,4 +1317,32 @@ class SimpleClientServerTests: XCTestCase {
         XCTAssertNoThrow(try self.clientChannel.finish())
         XCTAssertNoThrow(try self.serverChannel.finish())
     }
+
+    func testCachingInteractionWithMaxConcurrentStreams() throws {
+        // Here we test that having MAX_CONCURRENT_STREAMS higher than the cached closed streams does nothing.
+        // Also added for https://github.com/apple/swift-nio-http2/pull/11/
+        let maxCachedClosedStreams = 64
+
+        // Begin by getting the connection up.
+        try self.basicHTTP2Connection(maxCachedClosedStreams: maxCachedClosedStreams)
+
+        // Obtain some request data.
+        let requestHeaders = HTTPHeaders([(":path", "/"), (":method", "POST"), (":scheme", "https"), (":authority", "localhost")])
+        var requestBody = self.clientChannel.allocator.buffer(capacity: 128)
+        requestBody.write(staticString: "A simple HTTP/2 request.")
+
+        // Here we're going to issue exactly the number of streams we're willing to cache.
+        let clientStreamIDs = (0..<(maxCachedClosedStreams - 1)).map { _ in HTTP2StreamID() }
+        let clientHeadersFrames = clientStreamIDs.map { HTTP2Frame(streamID: $0, payload: .headers(requestHeaders)) }
+        try self.assertFramesRoundTrip(frames: clientHeadersFrames, sender: self.clientChannel, receiver: self.serverChannel)
+
+        // Now we send one more. In the bad code, this crashes.
+        let finalStreamID = HTTP2StreamID()
+        let explosionFrame = HTTP2Frame(streamID: finalStreamID, payload: .headers(requestHeaders))
+        try self.assertFramesRoundTrip(frames: [explosionFrame], sender: self.clientChannel, receiver: self.serverChannel)
+
+        // If we got here, all is well. We can tear down.
+        XCTAssertNoThrow(try self.clientChannel.finish())
+        XCTAssertNoThrow(try self.serverChannel.finish())
+    }
 }