diff --git a/instrumentation/aws_sdk/test/opentelemetry/patches/telemetry_test.rb b/instrumentation/aws_sdk/test/opentelemetry/patches/telemetry_test.rb
index 55fd838864..1bff99c618 100644
--- a/instrumentation/aws_sdk/test/opentelemetry/patches/telemetry_test.rb
+++ b/instrumentation/aws_sdk/test/opentelemetry/patches/telemetry_test.rb
@@ -39,7 +39,7 @@
     describe 'Lambda' do
       let(:service_name) { 'Lambda' }
       let(:service_uri) do
-        'https://lambda.us-east-1.amazonaws.com/2015-03-31/functions/'
+        'https://lambda.us-east-1.amazonaws.com/2015-03-31/functions'
       end
       let(:client) do
         Aws::Lambda::Client.new(
@@ -82,7 +82,7 @@
 
       it 'creates spans with all the non-stubbed parameters' do
         skip unless TestHelper.telemetry_plugin?(service_name)
-        stub_request(:get, 'https://lambda.us-east-1.amazonaws.com/2015-03-31/functions/')
+        stub_request(:get, 'https://lambda.us-east-1.amazonaws.com/2015-03-31/functions')
 
         client = Aws::Lambda::Client.new(
           telemetry_provider: otel_provider,
diff --git a/instrumentation/net_http/test/opentelemetry/instrumentation/net/http/instrumentation_test.rb b/instrumentation/net_http/test/opentelemetry/instrumentation/net/http/instrumentation_test.rb
index fb4d61a92a..e3961349d5 100644
--- a/instrumentation/net_http/test/opentelemetry/instrumentation/net/http/instrumentation_test.rb
+++ b/instrumentation/net_http/test/opentelemetry/instrumentation/net/http/instrumentation_test.rb
@@ -151,6 +151,7 @@
       end
 
       it 'does not create a span on connect when request ignored using a regexp' do
+        # this works because http://bazqux.com is reachable site; try http://asdfasdfsef.com will fail
         uri = URI.parse('http://bazqux.com')
         http = Net::HTTP.new(uri.host, uri.port)
         http.send(:connect)
@@ -169,7 +170,16 @@
       it 'creates a span on connect for a non-ignored request' do
         uri = URI.parse('http://example.com')
         http = Net::HTTP.new(uri.host, uri.port)
-        http.send(:connect)
+
+        fake_socket = Object.new
+        def fake_socket.setsockopt(*args); end
+        def fake_socket.close; end
+
+        # Replace the TCP socket creation with our fake socket
+        TCPSocket.stub(:open, fake_socket) do
+          http.send(:connect)
+        end
+
         http.send(:do_finish)
         _(exporter.finished_spans.size).must_equal 1
         _(span.name).must_equal('connect')
@@ -199,6 +209,10 @@
         OpenTelemetry::Common::Utilities.untraced do
           uri = URI.parse('http://example.com/body')
           http = Net::HTTP.new(uri.host, uri.port)
+
+          # Mock the connect
+          http.define_singleton_method(:connect) { true }
+
           http.send(:connect)
           http.send(:do_finish)
         end