diff --git a/src/taskgraph/optimize/base.py b/src/taskgraph/optimize/base.py
index ba07ca276..fc655f998 100644
--- a/src/taskgraph/optimize/base.py
+++ b/src/taskgraph/optimize/base.py
@@ -301,6 +301,18 @@ def replace_tasks(
         target_task_graph.graph.links_and_reverse_links_dict()
     )
 
+    # Many tasks share dependents (e.g. docker images or toolchains), so
+    # resolve the deadline of each dependent only once.
+    now = datetime.datetime.now(datetime.timezone.utc)
+    deadlines = {}
+
+    def get_deadline(label):
+        if label not in deadlines:
+            deadlines[label] = resolve_timestamps(
+                now, target_task_graph.tasks[label].task["deadline"]
+            )
+        return deadlines[label]
+
     for label in target_task_graph.graph.visit_postorder():
         logger.debug(f"replace_tasks: {label}")
         # if we're not allowed to optimize, that's easy..
@@ -331,14 +343,9 @@ def replace_tasks(
         opt_by, opt, arg = optimizations(label)
 
         # compute latest deadline of dependents (if any)
-        dependents = [target_task_graph.tasks[l] for l in dependents_of[label]]
         deadline = None
-        if dependents:
-            now = datetime.datetime.now(datetime.timezone.utc)
-            deadline = max(
-                resolve_timestamps(now, task.task["deadline"])
-                for task in dependents  # type: ignore
-            )
+        if dependents_of[label]:
+            deadline = max(get_deadline(l) for l in dependents_of[label])
 
         if isinstance(opt, IndexSearch):
             arg = arg, index_to_taskid, taskid_to_status
diff --git a/src/taskgraph/optimize/strategies.py b/src/taskgraph/optimize/strategies.py
index 8fed9e54a..459412c8a 100644
--- a/src/taskgraph/optimize/strategies.py
+++ b/src/taskgraph/optimize/strategies.py
@@ -1,3 +1,4 @@
+import functools
 import logging
 from datetime import datetime
 
@@ -10,6 +11,13 @@
 logger = logging.getLogger("optimization")
 
 
+@functools.cache
+def _parse_time(timestamp, fmt):
+    # Many tasks share the same deadline or replacement task, so avoid parsing
+    # the same timestamps over and over.
+    return datetime.strptime(timestamp, fmt)
+
+
 @register_strategy("index-search")
 class IndexSearch(OptimizationStrategy):
     # A task with no dependencies remaining after optimization will be replaced
@@ -56,10 +64,10 @@ def should_replace_task(self, task, params, deadline, arg):
                     )
                     continue
 
-                if deadline and datetime.strptime(
+                if deadline and _parse_time(
                     status["expires"],  # type: ignore
                     self.fmt,
-                ) < datetime.strptime(deadline, self.fmt):
+                ) < _parse_time(deadline, self.fmt):
                     logger.debug(
                         f"not replacing {task.label} with {task_id} because it expires before {deadline}"
                     )