diff --git a/sgx-bwmsgsv2.rb b/sgx-bwmsgsv2.rb
index 41c695a0210c153051166431d5c0a9367a06d4d6..78627a8fec8d8634ca6cabfd2d812607688be3ca 100755
--- a/sgx-bwmsgsv2.rb
+++ b/sgx-bwmsgsv2.rb
@@ -321,6 +321,10 @@ module SGXbwmsgsv2
 
 		msg.add_child(x)
 
+		store = Nokogiri::XML::Node.new 'store', msg.document
+		store['xmlns'] = 'urn:xmpp:hints'
+		msg.add_child(store)
+
 		write(msg)
 	rescue Exception => e
 		panic(e)
diff --git a/test/property/rantly_extensions/data_extensions.rb b/test/property/rantly_extensions/data_extensions.rb
index aeaec508c70b6eeeca61b22ef4004d8240cc1ae2..09755b2909f0e1a44ba9a7e6559e6a442ba905e8 100644
--- a/test/property/rantly_extensions/data_extensions.rb
+++ b/test/property/rantly_extensions/data_extensions.rb
@@ -109,14 +109,25 @@ class Rantly
 				)
 			end
 
+			# @return [Array<String>]
+			DELIVERABLE_MEDIA_EXTENSIONS = %w[.jpg .png .gif .mp4 .pdf].freeze
+			# @return [Array<String>]
+			CARRIER_MEDIA_EXTENSIONS = %w[.smil .txt .xml].freeze
+
+			# @param extensions [Array<String>]
 			# @return [String]
-			def media_url
+			def media_url(extensions: DELIVERABLE_MEDIA_EXTENSIONS + CARRIER_MEDIA_EXTENSIONS)
 				user_id = sized(range(3, 10)) { string(:alnum) }
 				name = sized(range(3, 12)) { string(:alnum) }
-				ext = choose(".jpg", ".png", ".gif", ".mp4", ".pdf", ".smil", ".txt", ".xml")
+				ext = choose(*extensions)
 				"https://messaging.bandwidth.com/api/v2/users/#{user_id}/media/#{name}#{ext}"
 			end
 
+			# @return [String]
+			def deliverable_media_url
+				media_url(extensions: DELIVERABLE_MEDIA_EXTENSIONS)
+			end
+
 			# @param ascii_only [Boolean, nil] truthy=force ASCII, nil=random
 			# @param nil_pct [Integer] weight (out of 100) for nil result
 			# @param empty_pct [Integer] weight (out of 100) for empty string result
diff --git a/test/property/test_webhook_handler.rb b/test/property/test_webhook_handler.rb
index 6d07956ab920586163dbcc228b306d4853e78b41..6e5b0a073031c6e20ca2ad14270b3b18c8d40338 100644
--- a/test/property/test_webhook_handler.rb
+++ b/test/property/test_webhook_handler.rb
@@ -526,4 +526,40 @@ class WebhookPropertyTest < Minitest::Test
 		}
 	end
 	em :test_inbound_nil_text_with_media_multi_recipient_writes_empty_body
+
+	def test_inbound_media_stanzas_include_store_hint
+		property_of {
+			Webhook
+				.new(REDIS)
+				.type { "message-received" }
+				.message { |registered, jid, dir, top_level_to|
+					Message
+						.new(REDIS)
+						.to {
+							array(integer(2)) { nanpa_phone } +
+								[top_level_to] +
+								array(integer(2)) { nanpa_phone }
+						}
+						.media { array(range(1, 3)) { deliverable_media_url } }
+						.generate(registered, jid, dir)
+				}
+				.generate
+		}.check { |metadata, example|
+			result = invoke_webhook(example)
+			assert_equal 200, result[0]
+
+			oob_stanzas = written.select { |s|
+				s.is_a?(Blather::Stanza::Message) &&
+					s.find_first("x")&.[]("xmlns") == "jabber:x:oob"
+			}
+			refute_empty oob_stanzas, "Should write at least one OOB stanza"
+
+			oob_stanzas.each do |msg|
+				store = msg.find_first("store")
+				assert_equal "urn:xmpp:hints", store&.[]("xmlns"),
+					"Every OOB stanza must include <store xmlns='urn:xmpp:hints'/>"
+			end
+		}
+	end
+	em :test_inbound_media_stanzas_include_store_hint
 end