diff --git a/Sources/NIOHPACK/HPACKHeader.swift b/Sources/NIOHPACK/HPACKHeader.swift
index 9b17a269..3406c98d 100644
--- a/Sources/NIOHPACK/HPACKHeader.swift
+++ b/Sources/NIOHPACK/HPACKHeader.swift
@@ -394,6 +394,9 @@ extension HPACKHeaders: CustomStringConvertible {
     }
 }
 
+// NOTE: This is a bad definition of equatable and hashable. In particular, both order and
+// indexability are ignored. We should change it, but we should be careful when we do so.
+// More discussion at https://github.com/apple/swift-nio-http2/issues/342.
 extension HPACKHeaders: Equatable {
     @inlinable
     public static func ==(lhs: HPACKHeaders, rhs: HPACKHeaders) -> Bool {
@@ -416,6 +419,22 @@ extension HPACKHeaders: Equatable {
     }
 }
 
+extension HPACKHeaders: Hashable {
+    @inlinable
+    public func hash(into hasher: inout Hasher) {
+        // Discriminator, to indicate that this is a collection. This improves the performance
+        // of Sets and Dictionaries that include collections of HPACKHeaders by reducing hash collisions.
+        hasher.combine(self.count)
+
+        // This emulates the logic used in equatability, but we sort it to ensure that
+        // we hash equivalently.
+        let names = Set(self.headers.lazy.map { $0.name }).sorted()
+        for name in names {
+            hasher.combine(self[name].sorted())
+        }
+    }
+}
+
 /// Defines the types of indexing and rewriting operations a decoder may take with
 /// regard to this header.
 public enum HPACKIndexing: CustomStringConvertible {
diff --git a/Tests/LinuxMain.swift b/Tests/LinuxMain.swift
index e989850c..13060b0e 100644
--- a/Tests/LinuxMain.swift
+++ b/Tests/LinuxMain.swift
@@ -43,6 +43,7 @@ class LinuxMainRunnerImpl: LinuxMainRunner {
              testCase(ConnectionStateMachineTests.allTests),
              testCase(ControlFrameBufferTests.allTests),
              testCase(HPACKCodingTests.allTests),
+             testCase(HPACKHeadersTests.allTests),
              testCase(HPACKIntegrationTests.allTests),
              testCase(HPACKRegressionTests.allTests),
              testCase(HTTP2ErrorTests.allTests),
diff --git a/Tests/NIOHPACKTests/HPACKHeadersTests+XCTest.swift b/Tests/NIOHPACKTests/HPACKHeadersTests+XCTest.swift
new file mode 100644
index 00000000..0f45f4ad
--- /dev/null
+++ b/Tests/NIOHPACKTests/HPACKHeadersTests+XCTest.swift
@@ -0,0 +1,34 @@
+//===----------------------------------------------------------------------===//
+//
+// This source file is part of the SwiftNIO open source project
+//
+// Copyright (c) 2017-2018 Apple Inc. and the SwiftNIO project authors
+// Licensed under Apache License v2.0
+//
+// See LICENSE.txt for license information
+// See CONTRIBUTORS.txt for the list of SwiftNIO project authors
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+//===----------------------------------------------------------------------===//
+//
+// HPACKHeadersTests+XCTest.swift
+//
+import XCTest
+
+///
+/// NOTE: This file was generated by generate_linux_tests.rb
+///
+/// Do NOT edit this file directly as it will be regenerated automatically when needed.
+///
+
+extension HPACKHeadersTests {
+
+   @available(*, deprecated, message: "not actually deprecated. Just deprecated to allow deprecated tests (which test deprecated functionality) without warnings")
+   static var allTests : [(String, (HPACKHeadersTests) -> () throws -> Void)] {
+      return [
+                ("testHPACKHeadersAreHashable", testHPACKHeadersAreHashable),
+           ]
+   }
+}
+
diff --git a/Tests/NIOHPACKTests/HPACKHeadersTests.swift b/Tests/NIOHPACKTests/HPACKHeadersTests.swift
new file mode 100644
index 00000000..bee09893
--- /dev/null
+++ b/Tests/NIOHPACKTests/HPACKHeadersTests.swift
@@ -0,0 +1,74 @@
+//===----------------------------------------------------------------------===//
+//
+// This source file is part of the SwiftNIO open source project
+//
+// Copyright (c) 2022 Apple Inc. and the SwiftNIO project authors
+// Licensed under Apache License v2.0
+//
+// See LICENSE.txt for license information
+// See CONTRIBUTORS.txt for the list of SwiftNIO project authors
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+//===----------------------------------------------------------------------===//
+
+import XCTest
+import NIOCore
+import NIOHPACK
+
+final class HPACKHeadersTests: XCTestCase {
+    func testHPACKHeadersAreHashable() throws {
+        let firstHeaders = HPACKHeaders([
+            (":foo", "bar"),
+            (":bar", "baz"),
+            ("boz", "box"),
+            ("fox", "fro"),
+        ])
+        // The same as firstHeaders but in a different order.
+        let secondHeaders = HPACKHeaders([
+            (":bar", "baz"),
+            (":foo", "bar"),
+            ("fox", "fro"),
+            ("boz", "box"),
+        ])
+        // Differs by one name from firstHeaders
+        let thirdHeaders = HPACKHeaders([
+            (":foo", "bar"),
+            (":bar", "baz"),
+            ("boz", "box"),
+            ("fax", "fro"),
+        ])
+        // Differs by one value from firstHeaders
+        let fourthHeaders = HPACKHeaders([
+            (":foo", "bar"),
+            (":bar", "baz"),
+            ("boz", "box"),
+            ("fox", "fra"),
+        ])
+
+        // First, confirm all things hash to themselves. This proves basic hashing correctness.
+        XCTAssertEqual(
+            Set([firstHeaders, firstHeaders]),
+            Set([firstHeaders])
+        )
+        XCTAssertEqual(
+            Set([secondHeaders, secondHeaders]),
+            Set([secondHeaders])
+        )
+        XCTAssertEqual(
+            Set([thirdHeaders, thirdHeaders]),
+            Set([thirdHeaders])
+        )
+        XCTAssertEqual(
+            Set([fourthHeaders, fourthHeaders]),
+            Set([fourthHeaders])
+        )
+
+        // Next, prove we can discriminate between different things. Here, importantly, secondHeaders is removed, as
+        // it hashes equal to firstHeaders.
+        XCTAssertEqual(
+            Set([firstHeaders, secondHeaders, thirdHeaders, fourthHeaders]),
+            Set([firstHeaders, thirdHeaders, fourthHeaders])
+        )
+    }
+}