diff --git a/update/job_runner_I2.py b/update/job_runner_I2.py
index 47f0a513..76dbde83 100644
--- a/update/job_runner_I2.py
+++ b/update/job_runner_I2.py
@@ -1,8 +1,10 @@
 import asyncio
+from collections import OrderedDict
 from dataclasses import dataclass
 from datetime import datetime, timedelta
+from enum import Enum
 import logging
-from typing import Optional
+from typing import Awaitable, Callable, Optional
 
 from temporalio import common, workflow, activity
 from temporalio.client import Client, WorkflowHandle
@@ -29,6 +31,23 @@ class JobOutput:
     stderr: str
 
 
+class TaskStatus(Enum):
+    BLOCKED = 1
+    UNBLOCKED = 2
+
+
+@dataclass
+class Task:
+    input: Job
+    handler: Callable[["JobRunner", Job], Awaitable[JobOutput]]
+    status: TaskStatus = TaskStatus.BLOCKED
+    output: Optional[JobOutput] = None
+
+    @property
+    def blocked(self) -> bool:
+        return self.status == TaskStatus.BLOCKED
+
+
 @workflow.defn
 class JobRunner:
     """
@@ -36,15 +55,73 @@ class JobRunner:
     not before `job.after_time`.
     """
 
+    def __init__(self) -> None:
+        self.task_queue = OrderedDict[JobID, Task]()
+        self.completed_tasks = set[JobID]()
+
+    def all_handlers_completed(self):
+        # We are considering adding an API like `all_handlers_completed` to SDKs. In this particular
+        # case, the user doesn't actually need the new API, since they are forced to track pending
+        # tasks in their queue implementation.
+        return not self.task_queue
+
+    # Note some undesirable things:
+    # 1. The update handler functions have become generic enqueuers; the "real" handler functions
+    #    are some other methods that don't have the @workflow.update decorator.
+    # 2. The update handler functions have to store a reference to the real handler in the queue.
+    # 3. The workflow `run` method is *much* more complicated and bug-prone here, compared to
+    #    I1:WaitUntilReadyToExecuteHandler
+
     @workflow.run
     async def run(self):
-        await workflow.wait_condition(
-            lambda: workflow.info().is_continue_as_new_suggested()
-        )
+        """
+        Process all tasks in the queue serially, in the main workflow coroutine.
+        """
+        # Note: there are many mistakes a user will make while trying to implement this workflow.
+        while not (
+            workflow.info().is_continue_as_new_suggested()
+            and self.all_handlers_completed()
+        ):
+            await workflow.wait_condition(lambda: bool(self.task_queue))
+            for id, task in list(self.task_queue.items()):
+                if task.status == TaskStatus.UNBLOCKED:
+                    await task.handler(self, task.input)
+                    del self.task_queue[id]
+                    self.completed_tasks.add(id)
+            for id, task in self.task_queue.items():
+                if task.status == TaskStatus.BLOCKED and self.ready_to_execute(
+                    task.input
+                ):
+                    task.status = TaskStatus.UNBLOCKED
         workflow.continue_as_new()
 
+    def ready_to_execute(self, job: Job) -> bool:
+        if not set(job.depends_on) <= self.completed_tasks:
+            return False
+        if after_time := job.after_time:
+            if float(after_time) > workflow.now().timestamp():
+                return False
+        return True
+
+    async def _enqueue_job_and_wait_for_result(
+        self, job: Job, handler: Callable[["JobRunner", Job], Awaitable[JobOutput]]
+    ) -> JobOutput:
+        task = Task(job, handler)
+        self.task_queue[job.id] = task
+        await workflow.wait_condition(lambda: task.output is not None)
+        # Footgun: a user might well think that they can record task completion here, but in fact it
+        # deadlocks.
+        # self.completed_tasks.add(job.id)
+        assert task.output
+        return task.output
+
     @workflow.update
     async def run_shell_script_job(self, job: Job) -> JobOutput:
+        return await self._enqueue_job_and_wait_for_result(
+            job, JobRunner._actually_run_shell_script_job
+        )
+
+    async def _actually_run_shell_script_job(self, job: Job) -> JobOutput:
         if security_errors := await workflow.execute_activity(
             run_shell_script_security_linter,
             args=[job.run],
@@ -58,6 +135,11 @@ async def run_shell_script_job(self, job: Job) -> JobOutput:
 
     @workflow.update
     async def run_python_job(self, job: Job) -> JobOutput:
+        return await self._enqueue_job_and_wait_for_result(
+            job, JobRunner._actually_run_python_job
+        )
+
+    async def _actually_run_python_job(self, job: Job) -> JobOutput:
         if not await workflow.execute_activity(
             check_python_interpreter_version,
             args=[job.python_interpreter_version],