diff --git a/CONTRIBUTING.md b/CONTRIBUTING.md
index f842720..a50c258 100644
--- a/CONTRIBUTING.md
+++ b/CONTRIBUTING.md
@@ -7,10 +7,13 @@ Thank you for your interest in contributing! This document covers everything you
 ```bash
 git clone https://github.com/bedrock-python/deadline-budget.git
 cd deadline-budget
-uv sync --group dev
+uv sync --group dev --all-extras
 uv run pre-commit install --hook-type commit-msg
 ```
 
+`--all-extras` installs Pydantic and Dishka. They are optional for users of the library but
+not for its test suite: without them `tests/unit/contrib/` fails at collection.
+
 ## Running checks
 
 ```bash
diff --git a/Makefile b/Makefile
index 9dd8fd8..ac0f6e8 100644
--- a/Makefile
+++ b/Makefile
@@ -1,7 +1,7 @@
 .PHONY: test test-unit test-integration fmt check build install docs-serve docs-build clean
 
 install:
-	uv sync --group dev
+	uv sync --group dev --all-extras
 
 fmt:
 	uv run ruff format .
diff --git a/deadline_budget/budget.py b/deadline_budget/budget.py
index 5114681..d2fd82e 100644
--- a/deadline_budget/budget.py
+++ b/deadline_budget/budget.py
@@ -71,13 +71,17 @@ def timeout_for(
     ) -> float:
         """Compute timeout for the next downstream call.
 
+        The remaining budget, less reserve_for_next, raised to min_timeout and then limited by cap.
+        Both bounds outrank what is left: min_timeout is returned even when the budget holds less
+        than that, and cap is applied last, so a cap below min_timeout wins over it.
+
         Args:
             cap: Maximum allowed timeout for this call (service-level cap).
             min_timeout: Minimum timeout override (default: use budget min_timeout).
             reserve_for_next: Reserve this many seconds for subsequent steps.
 
         Returns:
-            Computed timeout in seconds, bounded by [min_timeout, cap].
+            Computed timeout in seconds. May exceed the remaining budget when min_timeout does.
 
         Raises:
             DeadlineExceededError: If remaining budget is already exhausted.
diff --git a/deadline_budget/context.py b/deadline_budget/context.py
index 95d9bc9..830c826 100644
--- a/deadline_budget/context.py
+++ b/deadline_budget/context.py
@@ -35,9 +35,10 @@ def __init__(self, budget: DeadlineBudget, call_caps: dict[str, float]) -> None:
             budget: The underlying DeadlineBudget instance.
             call_caps: Mapping of call names to their timeout caps in seconds.
                 If a call is not in this dict, it will use remaining budget without cap.
+                Copied, so the context is not tied to the lifetime of the mapping given.
         """
         self._budget: DeadlineBudget = budget
-        self._call_caps: dict[str, float] = call_caps
+        self._call_caps: dict[str, float] = dict(call_caps)
 
     @classmethod
     def create(
@@ -76,8 +77,8 @@ def timeout_for_call(self, call_name: str, reserve_for_next: float = 0.0) -> flo
             reserve_for_next: Reserve this many seconds for subsequent steps.
 
         Returns:
-            Computed timeout in seconds, bounded by [min_timeout, call_cap] if cap exists,
-            or [min_timeout, remaining] if no cap configured.
+            Computed timeout in seconds, from DeadlineBudget.timeout_for with the configured cap.
+            May exceed the remaining budget when min_timeout does.
 
         Raises:
             DeadlineExceededError: If remaining budget is already exhausted.
@@ -115,5 +116,5 @@ def budget(self) -> DeadlineBudget:
 
     @property
     def call_caps(self) -> dict[str, float]:
-        """Access to configured call caps."""
+        """Access to this context's own copy of the configured call caps."""
         return self._call_caps
diff --git a/deadline_budget/contrib/dishka.py b/deadline_budget/contrib/dishka.py
index 53f5ba4..c01fbfc 100644
--- a/deadline_budget/contrib/dishka.py
+++ b/deadline_budget/contrib/dishka.py
@@ -95,7 +95,10 @@ def create_for_operation(self, operation: Any) -> BudgetContext:
 class DeadlineProvider(Provider):
     """Generic Dishka provider for request deadline budgeting.
 
-    Provides DeadlineContextFactory and optionally per-request BudgetContext.
+    Provides DeadlineContextFactory, and requires a DeadlineSettingsProtocol binding from one of
+    your own providers. It does not provide BudgetContext: a context belongs to one operation and
+    its countdown starts when it is built, so build it with DeadlineContextFactory.create_for_operation
+    where the request starts.
     """
 
     scope = Scope.APP
diff --git a/deadline_budget/contrib/settings.py b/deadline_budget/contrib/settings.py
index cb9c951..8236fcb 100644
--- a/deadline_budget/contrib/settings.py
+++ b/deadline_budget/contrib/settings.py
@@ -2,7 +2,7 @@
 
 from __future__ import annotations
 
-from pydantic import BaseModel, Field
+from pydantic import AliasChoices, BaseModel, Field
 
 
 class OperationDeadlineConfig(BaseModel):
@@ -28,6 +28,9 @@ class OperationDeadlineConfig(BaseModel):
     )
     calls_caps: dict[str, float] = Field(
         default_factory=dict,
+        # "call_caps" is the spelling BudgetContext uses; accepted here so the near-miss
+        # does not silently build a config with no caps at all.
+        validation_alias=AliasChoices("calls_caps", "call_caps"),
         description="Per-call timeout caps (key: call_name, value: seconds)",
     )
 
diff --git a/docs/agents.md b/docs/agents.md
index 46d1773..45f326a 100644
--- a/docs/agents.md
+++ b/docs/agents.md
@@ -134,10 +134,10 @@ classmethod instead:
 | `timeout_for_call(call_name, reserve_for_next=0.0)` | `float` | `budget.timeout_for(cap=call_caps.get(call_name), reserve_for_next=…)`. An unknown name is not an error — it means no cap. |
 | `check_expired()` / `remaining()` / `elapsed()` / `expired()` | as above | Straight delegation to the budget. |
 | `budget` (property) | `DeadlineBudget` | The underlying budget, for anything the context does not expose. |
-| `call_caps` (property) | `dict[str, float]` | The live mapping, not a copy. |
+| `call_caps` (property) | `dict[str, float]` | The context's own mapping — a copy of what was passed in, live for every later call on this context. |
 
 There is no `timeout_for` on `BudgetContext` and no `call_caps` mutator; reach through
-`ctx.budget` or edit the dict you passed in.
+`ctx.budget`, or mutate `ctx.call_caps` in place.
 
 ### `deadline_budget.contrib.settings` — extra `settings`, needs Pydantic 2
 
@@ -146,7 +146,7 @@ environment variables of their own.
 
 | Name | Fields |
 |---|---|
-| `OperationDeadlineConfig` | `budget_timeout: float = 10.0` (1.0–60.0), `safety_margin: float | None = None` (0.0–5.0), `min_timeout: float | None = None` (0.01–1.0), `calls_caps: dict[str, float] = {}` |
+| `OperationDeadlineConfig` | `budget_timeout: float = 10.0` (1.0–60.0), `safety_margin: float | None = None` (0.0–5.0), `min_timeout: float | None = None` (0.01–1.0), `calls_caps: dict[str, float] = {}` (also accepted as `call_caps` on input) |
 | `BaseDeadlineSettings` | `operations: dict[str, OperationDeadlineConfig] = {}`, `default_budget_timeout: float = 10.0`, `default_safety_margin: float = 0.5`, `default_min_timeout: float = 0.1` |
 
 `BaseDeadlineSettings.config_for_operation(operation)` returns the entry for that name, or
@@ -250,10 +250,11 @@ watching the clock.
 8. **An unknown `call_name` is not an error.** `timeout_for_call("typo")` returns the full
    remaining budget, uncapped. Caps are looked up with `dict.get`, so a misspelled or
    renamed key removes the ceiling instead of reporting it. Keep the keys in one constant.
-9. **The settings field is `calls_caps`; the context argument is `call_caps`.** The names
-   differ by one letter and Pydantic ignores unknown keys by default, so
-   `OperationDeadlineConfig(call_caps={...})` builds a config with no caps at all and no
-   complaint.
+9. **The settings field is `calls_caps`; the context argument is `call_caps`.**
+   `OperationDeadlineConfig` accepts either spelling as input and stores the value under
+   `calls_caps` — that is the name to read it back under, the name it dumps to, and the
+   name `OperationDeadlineConfigProtocol` requires. Every other field is matched exactly,
+   and Pydantic still ignores keys it does not know.
 10. **`BaseDeadlineSettings` is a `BaseModel`, not a `BaseSettings`,** despite the extra
     being called `settings`. It reads no environment and no `.env`; nest it inside your own
     `pydantic_settings.BaseSettings` if you want that.
@@ -264,8 +265,11 @@ watching the clock.
 12. **A budget is immutable after construction**, so reading it from several tasks or
     threads is safe. What is not safe is assuming those readers are sharing the time: see
     fan-out above.
-13. **`ctx.call_caps` is the live dict.** Mutating what you get back — or the dict you
-    passed to `create()` — changes the caps for every later call.
+13. **`ctx.call_caps` is the context's own dict.** The mapping handed to `BudgetContext`
+    is copied at construction, so changing the dict you passed to `create()` afterwards
+    changes nothing — and a context built from settings cannot write back into them.
+    Mutating what the property returns does change the caps for every later call, on that
+    context only.
 14. **The contrib modules are not re-exported.** `deadline_budget` exports exactly
     `DeadlineBudget`, `BudgetContext` and `DeadlineExceededError`. Everything else is
     imported from `deadline_budget.contrib.settings` or `deadline_budget.contrib.dishka`,
diff --git a/docs/guide/configuration.md b/docs/guide/configuration.md
index 07b043b..8cedac8 100644
--- a/docs/guide/configuration.md
+++ b/docs/guide/configuration.md
@@ -35,6 +35,10 @@ budget = DeadlineBudget(total_seconds=10.0, min_timeout=0.1)
 timeout = budget.timeout_for()
 ```
 
+The floor outranks the budget: `timeout_for()` returns `min_timeout` even when less than that
+is left, so the last call before exhaustion can overrun the deadline by up to `min_timeout`.
+That is what the safety margin pays for.
+
 #### `safety_margin` (optional, default: 0.0)
 
 Reserve time subtracted from total budget to prevent deadline violations:
@@ -53,10 +57,10 @@ budget = DeadlineBudget(total_seconds=10.0, safety_margin=0.5)
 Compute timeout for next downstream call.
 
 ```python
-# No cap: returns remaining budget (or min_timeout if less)
+# No cap: returns remaining budget (or min_timeout if remaining is less)
 timeout = budget.timeout_for()
 
-# With cap: returns min(cap, remaining)
+# With cap: returns min(cap, remaining), and min_timeout if remaining is less than that
 timeout = budget.timeout_for(cap=5.0)
 
 # Reserve budget for subsequent calls
@@ -73,6 +77,22 @@ timeout = budget.timeout_for(min_timeout=0.5)
 
 **Returns:** `float` — timeout in seconds
 
+**Precedence.** The whole computation is:
+
+```python
+available = max(remaining - reserve_for_next, min_timeout)
+timeout = min(available, cap) if cap is not None else available
+```
+
+Two consequences worth knowing before picking numbers:
+
+- **The floor outranks the budget.** With 0.4s left and `min_timeout=1.0`, `timeout_for()`
+  returns 1.0 — more time than the budget has. `reserve_for_next` disappears the same way:
+  when `remaining - reserve_for_next` falls under the floor, the floor wins and nothing is
+  reserved.
+- **The cap outranks the floor.** The cap is applied last, so `timeout_for(cap=0.05)` with
+  `min_timeout=0.1` returns 0.05. A service-level cap is never widened to reach the floor.
+
 ## BudgetContext Configuration
 
 ### Creation
@@ -113,6 +133,9 @@ ctx = BudgetContext.create(total_seconds=10.0, call_caps=call_caps)
 - Configured calls: Uses `min(cap, remaining_budget)`
 - Unconfigured calls: Uses `remaining_budget`
 
+Both go through `timeout_for()` and follow its precedence rules above, so `min_timeout` still
+applies underneath and a cap below `min_timeout` still wins.
+
 #### `min_timeout` (optional, default: 0.1)
 
 Minimum timeout (same as `DeadlineBudget`).
diff --git a/docs/guide/integrations.md b/docs/guide/integrations.md
index 3ce6e62..9bffb69 100644
--- a/docs/guide/integrations.md
+++ b/docs/guide/integrations.md
@@ -6,9 +6,17 @@ Extensions for deadline-budget with popular libraries.
 
 Install with: `pip install deadline-budget[settings]`
 
+Despite the name of the extra, `BaseDeadlineSettings` and `OperationDeadlineConfig` are plain
+`pydantic.BaseModel` classes, not `pydantic_settings.BaseSettings`. They read no environment
+variables and no `.env` file of their own; they hold the values you give them. Nest them in
+whatever your application already loads configuration into — a `BaseSettings` subclass if that
+is where your configuration comes from — as `AppSettings` does below.
+
 ### Configuration Classes
 
 ```python
+from pydantic import BaseModel, Field
+
 from deadline_budget.contrib.settings import BaseDeadlineSettings, OperationDeadlineConfig
 
 # Define settings
@@ -57,6 +65,10 @@ ctx = BudgetContext.create(
 )
 ```
 
+Note the spelling: the settings field is `calls_caps`, the `BudgetContext` argument is
+`call_caps`. `OperationDeadlineConfig` takes either spelling as input and stores it under
+`calls_caps`, which is the name to read it back under and the name it serialises to.
+
 ## Dishka DI Provider
 
 Install with: `pip install deadline-budget[dishka]`
diff --git a/docs/guide/quickstart.md b/docs/guide/quickstart.md
index 05aa153..57f93be 100644
--- a/docs/guide/quickstart.md
+++ b/docs/guide/quickstart.md
@@ -128,6 +128,10 @@ budget = DeadlineBudget(total_seconds=10.0, safety_margin=0.5)
 
 **Why use this?** Prevents returning timeouts that expire during network roundtrip.
 
+What you get back is the usable budget, not the total you passed: `budget.total_seconds` is
+9.5 here, and `DeadlineExceededError.budget_seconds` reports the same 9.5. Keep your own
+constant if a log line or a metric needs the 10.0.
+
 ### `min_timeout`
 
 Minimum timeout value returned by `timeout_for()`:
@@ -139,6 +143,9 @@ budget = DeadlineBudget(total_seconds=10.0, min_timeout=0.1)
 
 **Default:** 0.1 seconds
 
+The floor wins over the remaining budget, so the last call before exhaustion can be granted
+more time than is left. The safety margin pays for that.
+
 ### `cap`
 
 Maximum timeout for a specific call:
@@ -151,6 +158,10 @@ timeout = budget.timeout_for(cap=5.0)
 timeout = budget.timeout_for(cap=5.0)
 ```
 
+The cap is applied after the floor, so a cap below `min_timeout` wins over it:
+`timeout_for(cap=0.05)` with `min_timeout=0.1` returns 0.05. The
+[configuration guide](configuration.md) spells out the full precedence.
+
 ### `reserve_for_next`
 
 Reserve budget for subsequent calls:
diff --git a/tests/unit/contrib/test_dishka.py b/tests/unit/contrib/test_dishka.py
index fd50c49..1e4a92e 100644
--- a/tests/unit/contrib/test_dishka.py
+++ b/tests/unit/contrib/test_dishka.py
@@ -233,6 +233,28 @@ def test__factory__create_for_unknown_operation__uses_default_config() -> None:
     assert ctx.call_caps == {}
 
 
+def test__factory__context_caps_mutated__does_not_leak_into_the_next_context() -> None:
+    # Arrange
+    settings = MockSettings(
+        operations={
+            "signup": MockOperationConfig(
+                budget_timeout=10.0,
+                calls_caps={"identity_create": 3.0},
+            ),
+        }
+    )
+    factory = DeadlineContextFactory(settings)
+    first = factory.create_for_operation("signup")
+
+    # Act
+    first.call_caps["identity_create"] = 0.5
+
+    # Assert
+    second = factory.create_for_operation("signup")
+    assert second.call_caps == {"identity_create": 3.0}
+    assert settings.config_for_operation("signup").calls_caps == {"identity_create": 3.0}
+
+
 def test__deadline_provider__scope__is_app_scope() -> None:
     # Arrange
     provider = DeadlineProvider()
diff --git a/tests/unit/contrib/test_settings.py b/tests/unit/contrib/test_settings.py
index fee14b4..e36d920 100644
--- a/tests/unit/contrib/test_settings.py
+++ b/tests/unit/contrib/test_settings.py
@@ -43,6 +43,29 @@ def test__operation_config__with_custom_values__stores_all_fields() -> None:
     }
 
 
+def test__operation_config__with_call_caps_spelling__populates_calls_caps() -> None:
+    # Arrange
+    caps = {"identity_create_user": 3.0}
+
+    # Act
+    config = OperationDeadlineConfig(call_caps=caps)
+
+    # Assert
+    assert config.calls_caps == caps
+
+
+def test__operation_config__dump__keeps_calls_caps_as_the_field_name() -> None:
+    # Arrange
+    config = OperationDeadlineConfig(call_caps={"identity_create_user": 3.0})
+
+    # Act
+    dumped = config.model_dump()
+
+    # Assert
+    assert dumped["calls_caps"] == {"identity_create_user": 3.0}
+    assert "call_caps" not in dumped
+
+
 @pytest.mark.parametrize(
     "invalid_timeout,reason",
     [
diff --git a/tests/unit/test_context.py b/tests/unit/test_context.py
index 8449128..77ff183 100644
--- a/tests/unit/test_context.py
+++ b/tests/unit/test_context.py
@@ -36,6 +36,33 @@ def test__budget_context__create_without_caps__creates_context_with_empty_caps()
     assert ctx.call_caps == {}
 
 
+def test__budget_context__caps_mutated_after_create__keeps_the_caps_it_was_created_with() -> None:
+    # Arrange
+    call_caps = {"identity_create_user": 5.0}
+    ctx = BudgetContext.create(total_seconds=10.0, call_caps=call_caps)
+
+    # Act
+    call_caps["identity_create_user"] = 0.5
+    call_caps["credential_set_password"] = 0.5
+
+    # Assert
+    assert ctx.call_caps == {"identity_create_user": 5.0}
+    assert ctx.timeout_for_call("identity_create_user") == 5.0
+
+
+def test__budget_context__context_caps_mutated__leaves_the_caps_passed_in_untouched() -> None:
+    # Arrange
+    call_caps = {"identity_create_user": 5.0}
+    ctx = BudgetContext.create(total_seconds=10.0, call_caps=call_caps)
+
+    # Act
+    ctx.call_caps["identity_create_user"] = 0.5
+
+    # Assert
+    assert call_caps == {"identity_create_user": 5.0}
+    assert ctx.timeout_for_call("identity_create_user") == 0.5
+
+
 def test__budget_context__timeout_for_call_with_cap__applies_call_specific_cap() -> None:
     # Arrange
     call_caps = {