diff --git a/docs/src/Functions.md b/docs/src/Functions.md
index c37ace1..1f8ab9e 100644
--- a/docs/src/Functions.md
+++ b/docs/src/Functions.md
@@ -1,6 +1,9 @@
 # Functions
 
 ```@docs
+count_precompile_statements(
+    log::LambdaFunctionInvocationLog,
+  )
 create_lambda_function(
     remote_image::RemoteImage;
     role::Union{AWSRole, Nothing} = nothing,
@@ -103,8 +106,7 @@ run_local_image_test(
   )
 run_lambda_function_test(
     func::LambdaFunction,
-    function_argument::Any = "",
-    expected_response::Any = nothing;
+    function_test_data::FunctionTestData;
     check_function_state::Bool = false,
   )
 run_test(
diff --git a/src/Jot.jl b/src/Jot.jl
index f726bdc..be4f94c 100644
--- a/src/Jot.jl
+++ b/src/Jot.jl
@@ -46,6 +46,7 @@ export FunctionTestData
 export create_environment!
 export nest_quotes, create_sysimage
 export FunctionTestData
+export count_precompile_statements
 
 # CONSTANTS
 const docker_hash_limit = 12
@@ -204,6 +205,7 @@ function add_scripts_to_build_dir(
   )
   julia_args = [
     "--project=.",
+    "--trace-compile=stderr",
     ]
   if package_compile
     julia_args = vcat(julia_args, ["--sysimage=$SYSIMAGE_FNAME"])
@@ -537,8 +539,7 @@ end
 """
     run_lambda_function_test(
         func::LambdaFunction,
-        function_argument::Any = "",
-        expected_response::Any = nothing;
+        function_test_data::FunctionTestData;
         check_function_state::Bool = false,
       )::Tuple{Bool, Union{Missing, LambdaFunctionInvocationLog}}
 
@@ -549,15 +550,14 @@ pass, establishing only that the function can be contacted. Returns a tuple of `
 """
 function run_lambda_function_test(
     func::LambdaFunction,
-    function_argument::Any = "",
-    expected_response::Any = nothing;
+    function_test_data::FunctionTestData;
     check_function_state::Bool = false,
   )::Tuple{Bool, Union{Missing, LambdaFunctionInvocationLog}}
   try
     actual_response, log = invoke_function_with_log(
-        function_argument, func; check_state = check_function_state
+        function_test_data.test_argument, func; check_state = check_function_state
     )
-    passed = actual_response == expected_response
+    passed = actual_response == function_test_data.expected_response
     time_taken = get_invocation_run_time(log)
     passed && @info "Remote test passed in $time_taken ms; result received matched expected $actual_response"
     !passed && @info "Remote test failed; actual: $actual_response was not equal to expected: $expected_response"
diff --git a/src/LambdaFunctionInvocationLog.jl b/src/LambdaFunctionInvocationLog.jl
index 0e9ac7c..e92bc95 100644
--- a/src/LambdaFunctionInvocationLog.jl
+++ b/src/LambdaFunctionInvocationLog.jl
@@ -279,3 +279,20 @@ function get_invocation_run_time(report_event::LogEvent)::Float64
   parse(Float64, duration_str)
 end
 
+"""
+    count_precompile_statements(
+        log::LambdaFunctionInvocationLog,
+      )::Int64
+
+Counts the number of precompilation statements that were emitted during the Julia
+run-time. If the function has been precompiled or compiled with `PackageCompiler`,
+this should be zero.
+"""
+function count_precompile_statements(
+    log::LambdaFunctionInvocationLog,
+  )::Int64
+  precompile_events = filter(log.cloudwatch_log_events) do ev
+    startswith(ev.message, "precompile(")
+  end
+  length(precompile_events)
+end
diff --git a/test/runtests.jl b/test/runtests.jl
index 00cf5f4..0accbc3 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -175,7 +175,7 @@ function run_example_simple_test(clean_up::Bool)
     # ... and test it to see if it's working OK
     @info "Testing lambda function"
     @test run_lambda_function_test(
-      increment_vector_lambda, [2,3,4], [3,4,5]; check_function_state=true
+      increment_vector_lambda, FunctionTestData([2,3,4], [3,4,5]); check_function_state=true
     ) |> first
   end
   if clean_up
@@ -491,6 +491,7 @@ function run_multi_tests(
                 test_data.test_state.remote_image,
                 aws_role,
                 test_data.responder_function_test_args,
+                test_data.create_local_image_args.use_function_test_data,
                 skip_test_because_running_comparison_test_later,
               )
             end
@@ -627,15 +628,14 @@ end
 function compare_lambda_function_test_times(
     compiled::LambdaFunction,
     uncompiled::LambdaFunction,
-    test_arg::Any,
-    expected_response::Any,
+    function_test_data::FunctionTestData,
     repeat_num::Int64,
   )::Tuple{Float64, Float64}
   total_run_time = 0.0
   # Throw away first result, it's unrepresentative
-  _, _ = run_lambda_function_test(compiled, test_arg, expected_response)
+  _, _ = run_lambda_function_test(compiled, function_test_data)
   for num = 1:repeat_num
-    _, test_log = run_lambda_function_test(compiled, test_arg, expected_response)
+    _, test_log = run_lambda_function_test(compiled, function_test_data)
     this_run_time = get_invocation_run_time(test_log)
     @info "Test run $num with compiled local image took $this_run_time"
     total_run_time += this_run_time
@@ -644,9 +644,9 @@ function compare_lambda_function_test_times(
   @info "Average compiled run time was $average_compiled_run_time"
   total_run_time = 0.0
   # Throw away first result, it's unrepresentative
-  _, _ = run_lambda_function_test(uncompiled, test_arg, expected_response)
+  _, _ = run_lambda_function_test(uncompiled, function_test_data)
   for num = 1:repeat_num
-    _, test_log = run_lambda_function_test(uncompiled, test_arg, expected_response)
+    _, test_log = run_lambda_function_test(uncompiled, function_test_data)
     this_run_time = get_invocation_run_time(test_log)
     @info "Test run $num with uncompiled local image took $this_run_time"
     total_run_time += this_run_time
@@ -717,6 +717,7 @@ function test_lambda_function(
     remote_image::RemoteImage,
     aws_role::AWSRole,
     responder_function_test_args::ResponderFunctionTestArgs,
+    use_function_test_data::Bool,
     skip_test::Bool,
   )::LambdaFunction
   lambda_function = create_lambda_function(remote_image; role = aws_role)
@@ -725,15 +726,27 @@ function test_lambda_function(
   # Check that we can find it
   @test lambda_function in Jot.get_all_lambda_functions()
   if !skip_test
-    # Invoke it
+    # First invocation is exceptional, discard it
+    _ = run_lambda_function_test(
+      lambda_function,
+      to_function_test_data(responder_function_test_args);
+      check_function_state=true
+    )
+    sleep(5)
+    # Invoke it again
     (result, log) = run_lambda_function_test(
       lambda_function,
-      responder_function_test_args.good_arg,
-      responder_function_test_args.expected_response;
+      to_function_test_data(responder_function_test_args);
       check_function_state=true
     )
     @test result
     @info "Lambda function ran in $(get_invocation_run_time(log))"
+    # Unless FunctionTestData was not passed, check that there are no precopmiles
+    if use_function_test_data
+       @test count_precompile_statements(log) == 0
+    else
+       @test count_precompile_statements(log) > 0
+    end
     # Create the same thing using a remote image
     @test lambda_function == create_lambda_function(
       remote_image;
@@ -762,8 +775,7 @@ function test_compiled_lambda_function(
   (average_compiled_run_time, average_uncompiled_run_time) = compare_lambda_function_test_times(
     compiled_lambda_function,
     uncompiled_lambda_function,
-    responder_function_test_args.good_arg,
-    responder_function_test_args.expected_response,
+    to_function_test_data(responder_function_test_args),
     repeat_num,
   )
   @test average_compiled_run_time < (average_uncompiled_run_time / 2)