diff --git a/llvm/docs/CommandGuide/lit.rst b/llvm/docs/CommandGuide/lit.rst
--- a/llvm/docs/CommandGuide/lit.rst
+++ b/llvm/docs/CommandGuide/lit.rst
@@ -412,12 +412,16 @@
  **root** The root configuration.  This is the top-most :program:`lit` configuration in
  the project.
 
- **is_early** Whether the test suite as a whole should be given a head start
- before other test suites run.
-
- **early_tests** An explicit set of '/' separated test paths that should be
- given a head start before other tests run. For example, the top five or so
- slowest tests. See also: `--time-tests`
+ **start_phase** The phase of the test suite to start in. The default is zero
+ and tests are ordered from least to greatest. Therefore to have a simple head
+ start for all of the tests in the suite, set the value to -1. In general, it's
+ better to leave this value at zero and use `start_phases` instead.
+
+ **start_phases** A dictionary of '/' separated test paths (or path prefixes)
+ where the value is an offset to be added to the `start_phase` of a test suite.
+ For example: the top five or so slowest tests might be put in the `-1` offset;
+ and fast/low-reward tests might be put in the `+1` offset. See also:
+ `--time-tests`
 
  **pipefail** Normally a test using a shell pipe fails if any of the commands
  on the pipe fail. If this is not desired, setting this variable to false
diff --git a/llvm/test/Unit/lit.cfg.py b/llvm/test/Unit/lit.cfg.py
--- a/llvm/test/Unit/lit.cfg.py
+++ b/llvm/test/Unit/lit.cfg.py
@@ -13,8 +13,8 @@
 # suffixes: A list of file extensions to treat as test files.
 config.suffixes = []
 
-# is_early; Request to run this suite early.
-config.is_early = True
+# start_phase; Request to start this suite early.
+config.start_phase = -1
 
 # test_source_root: The root path where tests are located.
 # test_exec_root: The root path where tests should be run.
diff --git a/llvm/utils/lit/lit/Test.py b/llvm/utils/lit/lit/Test.py
--- a/llvm/utils/lit/lit/Test.py
+++ b/llvm/utils/lit/lit/Test.py
@@ -396,14 +396,19 @@
         identifiers = set(filter(BooleanExpression.isIdentifier, tokens))
         return identifiers
 
-    def isEarlyTest(self):
+    def getTestPhase(self):
         """
-        isEarlyTest() -> bool
+        getTestPhase() -> int
 
-        Check whether this test should be executed early in a particular run.
-        This can be used for test suites with long running tests to maximize
-        parallelism or where it is desirable to surface their failures early.
+        Get the phase that a particular test should start in. This can be used
+        for test suites with long running tests to maximize concurrency or where
+        it is desirable to surface their failures early. It can also be used to
+        run fast and low reward tests late.
         """
-        if '/'.join(self.path_in_suite) in self.suite.config.early_tests:
-            return True
-        return self.suite.config.is_early
+
+        base_phase = self.suite.config.start_phase
+        for depth in range(len(self.path_in_suite), 0, -1):
+            path = '/'.join(self.path_in_suite[:depth])
+            if path in self.suite.config.start_phases:
+                return base_phase + self.suite.config.start_phases[path]
+        return base_phase
diff --git a/llvm/utils/lit/lit/TestingConfig.py b/llvm/utils/lit/lit/TestingConfig.py
--- a/llvm/utils/lit/lit/TestingConfig.py
+++ b/llvm/utils/lit/lit/TestingConfig.py
@@ -125,10 +125,9 @@
         # require one of the features in this list if this list is non-empty.
         # Configurations can set this list to restrict the set of tests to run.
         self.limit_to_features = set(limit_to_features)
-        # Whether the suite should be tested early in a given run.
-        self.is_early = bool(is_early)
-        # List of tests to run early.
-        self.early_tests = {}
+        # Phased start ordering of tests or test prefixes.
+        self.start_phase = -1 if is_early else 0
+        self.start_phases = {}
         self.parallelism_group = parallelism_group
         self._recursiveExpansionLimit = None
 
diff --git a/llvm/utils/lit/lit/cl_arguments.py b/llvm/utils/lit/lit/cl_arguments.py
--- a/llvm/utils/lit/lit/cl_arguments.py
+++ b/llvm/utils/lit/lit/cl_arguments.py
@@ -9,7 +9,7 @@
 
 
 class TestOrder(enum.Enum):
-    EARLY_TESTS_THEN_BY_NAME = enum.auto()
+    PHASE_THEN_BY_NAME = enum.auto()
     FAILING_FIRST = enum.auto()
     RANDOM = enum.auto()
 
@@ -209,7 +209,7 @@
     elif opts.incremental:
         opts.order = TestOrder.FAILING_FIRST
     else:
-        opts.order = TestOrder.EARLY_TESTS_THEN_BY_NAME
+        opts.order = TestOrder.PHASE_THEN_BY_NAME
 
     if opts.numShards or opts.runShard:
         if not opts.numShards or not opts.runShard:
diff --git a/llvm/utils/lit/lit/main.py b/llvm/utils/lit/lit/main.py
--- a/llvm/utils/lit/lit/main.py
+++ b/llvm/utils/lit/lit/main.py
@@ -160,8 +160,8 @@
 
 def determine_order(tests, order):
     from lit.cl_arguments import TestOrder
-    if order == TestOrder.EARLY_TESTS_THEN_BY_NAME:
-        tests.sort(key=lambda t: (not t.isEarlyTest(), t.getFullName()))
+    if order == TestOrder.PHASE_THEN_BY_NAME:
+        tests.sort(key=lambda t: (t.getTestPhase(), t.getFullName()))
     elif order == TestOrder.FAILING_FIRST:
         def by_mtime(test):
             return os.path.getmtime(test.getFilePath())
diff --git a/llvm/utils/lit/tests/Inputs/early-tests/lit.cfg b/llvm/utils/lit/tests/Inputs/early-tests/lit.cfg
deleted file mode 100644
--- a/llvm/utils/lit/tests/Inputs/early-tests/lit.cfg
+++ /dev/null
@@ -1,7 +0,0 @@
-import lit.formats
-config.name = 'early-tests'
-config.suffixes = ['.txt']
-config.test_format = lit.formats.ShTest()
-config.test_source_root = None
-config.test_exec_root = None
-config.early_tests = { "subdir/ccc.txt" }
diff --git a/llvm/utils/lit/tests/Inputs/start-phases/lit.cfg b/llvm/utils/lit/tests/Inputs/start-phases/lit.cfg
new file mode 100644
--- /dev/null
+++ b/llvm/utils/lit/tests/Inputs/start-phases/lit.cfg
@@ -0,0 +1,15 @@
+import lit.formats
+config.name = 'early-tests'
+config.suffixes = ['.txt']
+config.test_format = lit.formats.ShTest()
+config.test_source_root = None
+config.test_exec_root = None
+config.start_phases = {
+    "subdir" : -4,
+    "subdir/early.txt" : -3,
+    "test9.txt" : -2,
+    "test8.txt" : -1,
+    "test2.txt" : +1,
+    "test1.txt" : +2,
+    "subdir/late.txt" : +3,
+}
diff --git a/llvm/utils/lit/tests/Inputs/early-tests/aaa.txt b/llvm/utils/lit/tests/Inputs/start-phases/subdir/early.txt
rename from llvm/utils/lit/tests/Inputs/early-tests/aaa.txt
rename to llvm/utils/lit/tests/Inputs/start-phases/subdir/early.txt
diff --git a/llvm/utils/lit/tests/Inputs/early-tests/bbb.txt b/llvm/utils/lit/tests/Inputs/start-phases/subdir/late.txt
rename from llvm/utils/lit/tests/Inputs/early-tests/bbb.txt
rename to llvm/utils/lit/tests/Inputs/start-phases/subdir/late.txt
diff --git a/llvm/utils/lit/tests/Inputs/early-tests/subdir/ccc.txt b/llvm/utils/lit/tests/Inputs/start-phases/subdir/misc.txt
rename from llvm/utils/lit/tests/Inputs/early-tests/subdir/ccc.txt
rename to llvm/utils/lit/tests/Inputs/start-phases/subdir/misc.txt
diff --git a/llvm/utils/lit/tests/Inputs/start-phases/test1.txt b/llvm/utils/lit/tests/Inputs/start-phases/test1.txt
new file mode 100644
--- /dev/null
+++ b/llvm/utils/lit/tests/Inputs/start-phases/test1.txt
@@ -0,0 +1 @@
+# RUN: true
diff --git a/llvm/utils/lit/tests/Inputs/start-phases/test2.txt b/llvm/utils/lit/tests/Inputs/start-phases/test2.txt
new file mode 100644
--- /dev/null
+++ b/llvm/utils/lit/tests/Inputs/start-phases/test2.txt
@@ -0,0 +1 @@
+# RUN: true
diff --git a/llvm/utils/lit/tests/Inputs/start-phases/test5.txt b/llvm/utils/lit/tests/Inputs/start-phases/test5.txt
new file mode 100644
--- /dev/null
+++ b/llvm/utils/lit/tests/Inputs/start-phases/test5.txt
@@ -0,0 +1 @@
+# RUN: true
diff --git a/llvm/utils/lit/tests/Inputs/start-phases/test8.txt b/llvm/utils/lit/tests/Inputs/start-phases/test8.txt
new file mode 100644
--- /dev/null
+++ b/llvm/utils/lit/tests/Inputs/start-phases/test8.txt
@@ -0,0 +1 @@
+# RUN: true
diff --git a/llvm/utils/lit/tests/Inputs/start-phases/test9.txt b/llvm/utils/lit/tests/Inputs/start-phases/test9.txt
new file mode 100644
--- /dev/null
+++ b/llvm/utils/lit/tests/Inputs/start-phases/test9.txt
@@ -0,0 +1 @@
+# RUN: true
diff --git a/llvm/utils/lit/tests/early-tests.py b/llvm/utils/lit/tests/early-tests.py
deleted file mode 100644
--- a/llvm/utils/lit/tests/early-tests.py
+++ /dev/null
@@ -1,9 +0,0 @@
-## Check that we can run tests early.
-
-# RUN: %{lit} -j1 %{inputs}/early-tests | FileCheck %s
-
-# CHECK:     -- Testing: 3 tests, 1 workers --
-# CHECK-NEXT: PASS: early-tests :: subdir/ccc.txt
-# CHECK-NEXT: PASS: early-tests :: aaa.txt
-# CHECK-NEXT: PASS: early-tests :: bbb.txt
-# CHECK:     Passed: 3
diff --git a/llvm/utils/lit/tests/start-phases.py b/llvm/utils/lit/tests/start-phases.py
new file mode 100644
--- /dev/null
+++ b/llvm/utils/lit/tests/start-phases.py
@@ -0,0 +1,15 @@
+## Check that we can phase order the start of tests.
+
+# RUN: %{lit} -j1 %{inputs}/start-phases | FileCheck %s
+# END.
+
+# CHECK:     -- Testing: 8 tests, 1 workers --
+# CHECK-NEXT: PASS: early-tests :: subdir/misc.txt
+# CHECK-NEXT: PASS: early-tests :: subdir/early.txt
+# CHECK-NEXT: PASS: early-tests :: test9.txt
+# CHECK-NEXT: PASS: early-tests :: test8.txt
+# CHECK-NEXT: PASS: early-tests :: test5.txt
+# CHECK-NEXT: PASS: early-tests :: test2.txt
+# CHECK-NEXT: PASS: early-tests :: test1.txt
+# CHECK-NEXT: PASS: early-tests :: subdir/late.txt
+# CHECK:     Passed: 8
diff --git a/mlir/test/Unit/lit.cfg.py b/mlir/test/Unit/lit.cfg.py
--- a/mlir/test/Unit/lit.cfg.py
+++ b/mlir/test/Unit/lit.cfg.py
@@ -13,8 +13,8 @@
 # suffixes: A list of file extensions to treat as test files.
 config.suffixes = []
 
-# is_early; Request to run this suite early.
-config.is_early = True
+# start_phase; Request to start this suite early.
+config.start_phase = -1
 
 # test_source_root: The root path where tests are located.
 # test_exec_root: The root path where tests should be run.