diff --git a/docs/project/usage.md b/docs/project/usage.md
index 201a058..f968b5d 100644
--- a/docs/project/usage.md
+++ b/docs/project/usage.md
@@ -94,17 +94,31 @@ await micropip.install("pkg", deps=False)
 
 ### Constraining indirect dependencies
 
-Dependency resolution can be further customized with optional `constraints`: these
-provide the versions (or URLs of wheels)
+Dependency resolution can be further customized with optional `constraints`: as
+described in the [`pip`](https://pip.pypa.io/en/stable/user_guide/#constraints-files)
+documentation, these must provide a name and version (or URL), and may not request
+`[extras]`.
 
 ```python
-await micropip.install("pkg", constraints=["other-pkg ==0.1.1"])
+await micropip.install(
+    "pkg",
+    constraints=[
+        "other-pkg ==0.1.1",
+        "some-other-pkg <2",
+        "yet-another-pkg@https://example.com/yet_another_pkg-0.1.2-py3-none-any.whl",
+        # invalid examples                         # why?
+        # yet_another_pkg-0.1.2-py3-none-any.whl   # missing name
+        # something-completely[different] ==0.1.1  # extras
+        # package-with-no-version                  # missing version or URL
+    ]
+)
 ```
 
-Default `constraints` may be provided to be used by all subsequent calls to
-`micropip.install`:
+`micropip.set_constraints` replaces any default constraints for all subsequent
+calls to `micropip.install` that don't specify constraints:
 
 ```python
 micropip.set_constraints = ["other-pkg ==0.1.1"]
-await micropip.install("pkg")
+await micropip.install("pkg")                         # uses defaults
+await micropip.install("another-pkg", constraints=[]) # ignores defaults
 ```
diff --git a/micropip/transaction.py b/micropip/transaction.py
index c962396..3b0876f 100644
--- a/micropip/transaction.py
+++ b/micropip/transaction.py
@@ -38,13 +38,29 @@ class Transaction:
     verbose: bool | int | None = None
     constraints: list[str] | None = None
 
-    def __post_init__(self):
+    def __post_init__(self) -> None:
         # If index_urls is None, pyodide-lock.json have to be searched first.
         # TODO: when PyPI starts to support hosting WASM wheels, this might be deleted.
         self.search_pyodide_lock_first = (
             self.index_urls == package_index.DEFAULT_INDEX_URLS
         )
 
+        self.constrained_reqs: dict[str, Requirement] = {}
+
+        for constraint in self.constraints or []:
+            con = Requirement(constraint)
+            if not con.name:
+                logger.debug("Transaction: discarding nameless constraint: %s", con)
+                continue
+            if con.extras:
+                logger.debug("Transaction: discarding [extras] constraint: %s", con)
+                continue
+            if not con.url or len(con.specifier):
+                logger.debug("Transaction: discarding versionless constraint: %s", con)
+                continue
+            con.name = canonicalize_name(con.name)
+            self.constrained_reqs[con.name] = con
+
     async def gather_requirements(
         self,
         requirements: list[str] | list[Requirement],
@@ -88,6 +104,14 @@ def check_version_satisfied(self, req: Requirement) -> tuple[bool, str]:
             f"Requested '{req}', " f"but {req.name}=={ver} is already installed"
         )
 
+    def constrain_requirement(self, req: Requirement) -> Requirement:
+        """Provide a constrained requirement, if available, or the original."""
+        constrained_req = self.constrained_reqs.get(canonicalize_name(req.name))
+        if constrained_req:
+            logger.debug("Transaction: %s constrained to %s", req, constrained_req)
+            return constrained_req
+        return req
+
     async def add_requirement_inner(
         self,
         req: Requirement,
@@ -100,6 +124,8 @@ async def add_requirement_inner(
         for e in req.extras:
             self.ctx_extras.append({"extra": e})
 
+        req = self.constrain_requirement(req)
+
         if self.pre:
             req.specifier.prereleases = True
 
@@ -136,6 +162,7 @@ def eval_marker(e: dict[str, str]) -> bool:
                 eval_marker(e) for e in self.ctx_extras
             ):
                 return
+
         # Is some version of this package is already installed?
         req.name = canonicalize_name(req.name)