diff --git a/DESCRIPTION b/DESCRIPTION
index 78ce0de9..8929557f 100644
--- a/DESCRIPTION
+++ b/DESCRIPTION
@@ -1,6 +1,6 @@
 Package: monty
 Title: Monte Carlo Models
-Version: 0.2.11
+Version: 0.2.12
 Authors@R: c(person("Rich", "FitzJohn", role = c("aut", "cre"),
                     email = "rich.fitzjohn@gmail.com"),
              person("Wes", "Hinsley", role = "aut"),
diff --git a/R/dsl-generate.R b/R/dsl-generate.R
index 520291e3..01ac83d7 100644
--- a/R/dsl-generate.R
+++ b/R/dsl-generate.R
@@ -1,11 +1,14 @@
 dsl_generate <- function(dat) {
   env <- new.env(parent = asNamespace("monty"))
   env$packer <- monty_packer(dat$parameters)
+  env$fixed <- dat$fixed
 
   meta <- list(
     pars = quote(pars),
     data = quote(data),
-    density = quote(density))
+    density = quote(density),
+    fixed = quote(fixed),
+    fixed_contents = names(env$fixed))
 
   density <- dsl_generate_density(dat, env, meta)
   direct_sample <- dsl_generate_direct_sample(dat, env, meta)
@@ -110,7 +113,10 @@ dsl_generate_density_rewrite_lookup <- function(expr, dest, meta) {
                        dest, meta)
     as.call(expr)
   } else if (is.name(expr)) {
-    call("[[", meta[[dest]], as.character(expr))
+    if (as.character(expr) %in% meta$fixed_contents) {
+      dest <- meta$fixed
+    }
+    call("[[", meta[[as.character(dest)]], as.character(expr))
   } else {
     expr
   }
diff --git a/R/dsl-parse.R b/R/dsl-parse.R
index 1e0f1147..6968266d 100644
--- a/R/dsl-parse.R
+++ b/R/dsl-parse.R
@@ -1,16 +1,18 @@
 ## The default of gradient_required = TRUE here helps with tests
-dsl_parse <- function(exprs, gradient_required = TRUE, call = NULL) {
+dsl_parse <- function(exprs, gradient_required = TRUE, fixed = NULL,
+                      call = NULL) {
   exprs <- lapply(exprs, dsl_parse_expr, call)
 
   dsl_parse_check_duplicates(exprs, call)
-  dsl_parse_check_usage(exprs, call)
+  dsl_parse_check_fixed(exprs, fixed, call)
+  dsl_parse_check_usage(exprs, fixed, call)
 
   name <- vcapply(exprs, "[[", "name")
   parameters <- name[vcapply(exprs, "[[", "type") == "stochastic"]
 
   adjoint <- dsl_parse_adjoint(parameters, exprs, gradient_required)
 
-  list(parameters = parameters, exprs = exprs, adjoint = adjoint)
+  list(parameters = parameters, exprs = exprs, adjoint = adjoint, fixed = fixed)
 }
 
 
@@ -109,11 +111,28 @@ dsl_parse_check_duplicates <- function(exprs, call) {
 }
 
 
-dsl_parse_check_usage <- function(exprs, call) {
+dsl_parse_check_fixed <- function(exprs, fixed, call) {
+  if (is.null(fixed)) {
+    return()
+  }
+
+  name <- vcapply(exprs, "[[", "name")
+  err <- name %in% names(fixed)
+  if (any(err)) {
+    eq <- exprs[[which(err)[[1]]]]
+    dsl_parse_error(
+      "Value '{eq$name}' in 'fixed' is shadowed by {eq$type}",
+      "E207", eq$expr, call)
+  }
+}
+
+
+dsl_parse_check_usage <- function(exprs, fixed, call) {
   name <- vcapply(exprs, "[[", "name")
+  names_fixed <- names(fixed)
   for (i in seq_along(exprs)) {
     e <- exprs[[i]]
-    err <- setdiff(e$depends, name[seq_len(i - 1)])
+    err <- setdiff(e$depends, c(name[seq_len(i - 1)], names_fixed))
     if (length(err) > 0) {
       ## Out of order:
       out_of_order <- intersect(name, err)
@@ -124,6 +143,8 @@ dsl_parse_check_usage <- function(exprs, call) {
         ## Could also tell the user about variables found in the
         ## calling env, but that requires detecting and then passing
         ## through the correct environment.
+        ##
+        ## Could also tell about near misses.
         context <- NULL
       }
       ## TODO: It would be nice to indicate that we want to highlight
diff --git a/R/dsl.R b/R/dsl.R
index 419bd224..f0e67648 100644
--- a/R/dsl.R
+++ b/R/dsl.R
@@ -23,6 +23,16 @@
 ##'   then we will error if it is not possible to create a gradient
 ##'   function.
 ##'
+##' @param fixed An optional list of values that can be used within
+##'   the DSL code.  Anything you provide here is available for your
+##'   calculations.  In the interest of future compatibility, we check
+##'   currently that all elements are scalars.  In future this may
+##'   become more flexible and allow passing environments, etc.  Once
+##'   provided, these values cannot be changed without rebuilding the
+##'   model; they are fixed data.  You might use these for
+##'   hyperparameters that are fixed across a set of model runs, for
+##'   example.
+##'
 ##' @return A [monty_model] object derived from the expressions you
 ##'   provide.
 ##'
@@ -38,7 +48,7 @@
 ##'
 ##' # You can also pass strings
 ##' monty_dsl("a ~ Normal(0, 1)")
-monty_dsl <- function(x, type = NULL, gradient = NULL) {
+monty_dsl <- function(x, type = NULL, gradient = NULL, fixed = NULL) {
   quo <- rlang::enquo(x)
   if (rlang::quo_is_symbol(quo)) {
     x <- rlang::eval_tidy(quo)
@@ -46,14 +56,15 @@ monty_dsl <- function(x, type = NULL, gradient = NULL) {
     x <- rlang::quo_get_expr(quo)
   }
   call <- environment()
+  fixed <- check_dsl_fixed(fixed)
   exprs <- dsl_preprocess(x, type, call)
-  dat <- dsl_parse(exprs, gradient, call)
+  dat <- dsl_parse(exprs, gradient, fixed, call)
   dsl_generate(dat)
 }
 
 
 
-monty_dsl_parse <- function(x, type = NULL, gradient = NULL) {
+monty_dsl_parse <- function(x, type = NULL, gradient = NULL, fixed = NULL) {
   call <- environment()
   quo <- rlang::enquo(x)
   if (rlang::quo_is_symbol(quo)) {
@@ -61,8 +72,9 @@ monty_dsl_parse <- function(x, type = NULL, gradient = NULL) {
   } else {
     x <- rlang::quo_get_expr(quo)
   }
+  fixed <- check_dsl_fixed(fixed, call)
   exprs <- dsl_preprocess(x, type, call)
-  dsl_parse(exprs, gradient, call)
+  dsl_parse(exprs, gradient, fixed, call)
 }
 
 
@@ -154,3 +166,25 @@ monty_dsl_parse_distribution <- function(expr, name = NULL) {
   list(success = TRUE,
        value = value)
 }
+
+
+check_dsl_fixed <- function(fixed, call) {
+  if (is.null(fixed)) {
+    return(NULL)
+  }
+  assert_list(fixed, call = call)
+  if (length(fixed) == 0) {
+    return(NULL)
+  }
+  assert_named(fixed, unique = TRUE, call = call)
+  err <- lengths(fixed) != 1
+  if (any(err)) {
+    info <- sprintf("'%s' had length %d",
+                    names(fixed)[err], lengths(fixed[err]))
+    cli::cli_abort(
+      c("All elements of 'fixed' must currently be scalars",
+        set_names(info, "x")),
+      arg = "fixed", call = call)
+  }
+  fixed
+}
diff --git a/R/sysdata.rda b/R/sysdata.rda
index 4c9f4fd9..6e7a88bd 100644
Binary files a/R/sysdata.rda and b/R/sysdata.rda differ
diff --git a/man/monty_dsl.Rd b/man/monty_dsl.Rd
index 352799fe..7edd127b 100644
--- a/man/monty_dsl.Rd
+++ b/man/monty_dsl.Rd
@@ -4,7 +4,7 @@
 \alias{monty_dsl}
 \title{Domain Specific Language for monty}
 \usage{
-monty_dsl(x, type = NULL, gradient = NULL)
+monty_dsl(x, type = NULL, gradient = NULL, fixed = NULL)
 }
 \arguments{
 \item{x}{The model as an expression.  This may be given as an
@@ -26,6 +26,16 @@ attempt to construct a gradient function, which prevents a
 warning being generated if this is not possible.  If \code{TRUE},
 then we will error if it is not possible to create a gradient
 function.}
+
+\item{fixed}{An optional list of values that can be used within
+the DSL code.  Anything you provide here is available for your
+calculations.  In the interest of future compatibility, we check
+currently that all elements are scalars.  In future this may
+become more flexible and allow passing environments, etc.  Once
+provided, these values cannot be changed without rebuilding the
+model; they are fixed data.  You might use these for
+hyperparameters that are fixed across a set of model runs, for
+example.}
 }
 \value{
 A \link{monty_model} object derived from the expressions you
diff --git a/tests/testthat/test-dsl-parse.R b/tests/testthat/test-dsl-parse.R
index ef1af335..0146eb60 100644
--- a/tests/testthat/test-dsl-parse.R
+++ b/tests/testthat/test-dsl-parse.R
@@ -210,3 +210,32 @@ test_that("can explain an error", {
     mockery::mock_args(mock_explain)[[1]],
     list(dsl_errors, "E101", "pretty"))
 })
+
+
+test_that("empty fixed data is null", {
+  expect_null(check_dsl_fixed(NULL))
+  expect_null(check_dsl_fixed(list()))
+})
+
+
+test_that("validate fixed data for dsl", {
+  expect_error(
+    check_dsl_fixed(c(a = 1, b = 2)),
+    "Expected 'fixed' to be a list")
+  expect_error(
+    check_dsl_fixed(list(a = 1, b = 2, a = 2)),
+    "'fixed' must have unique names")
+  expect_error(
+    check_dsl_fixed(list(a = 1, b = 2:3, c = numeric(10))),
+    "All elements of 'fixed' must currently be scalars")
+  expect_equal(
+    check_dsl_fixed(list(a = 1, b = 2)),
+    list(a = 1, b = 2))
+})
+
+
+test_that("assignments cannot shadow names of fixed variables", {
+  expect_error(
+    dsl_parse(list(quote(a <- 1)), fixed = list(a = 1)),
+    "Value 'a' in 'fixed' is shadowed by assignment")
+})
diff --git a/tests/testthat/test-dsl.R b/tests/testthat/test-dsl.R
index 99ba74f5..51afcd5b 100644
--- a/tests/testthat/test-dsl.R
+++ b/tests/testthat/test-dsl.R
@@ -142,3 +142,11 @@ test_that("can compute gradients of complicated models", {
 
   expect_equal(m$gradient(p), numDeriv::grad(m$density, p))
 })
+
+
+test_that("can use fixed data in dsl", {
+  m <- monty_dsl({
+    a ~ Normal(mu, sd)
+  }, fixed = list(mu = 1, sd = 2))
+  expect_equal(m$density(0), dnorm(0, 1, 2, log = TRUE))
+})
diff --git a/vignettes/dsl-errors.Rmd b/vignettes/dsl-errors.Rmd
index 1f2115bc..c38da621 100644
--- a/vignettes/dsl-errors.Rmd
+++ b/vignettes/dsl-errors.Rmd
@@ -125,3 +125,7 @@ Variables are used out of order.  If you are using odin this is a big departure
 # `E206`
 
 Failed to differentiate the model.  This error will only be seen where it was not possible to differentiate your model but you requested that a gradient be available.  Not all functions supported in the DSL can currently be differentiated by monty; if you think that yours should be, please let us know.
+
+# `E207`
+
+A value in `fixed` is shadowed by an assignment or a relationship.  If you pass in fixed data it may not be used on the left hand side of any expression in your DSL code.
diff --git a/vignettes/dsl.Rmd b/vignettes/dsl.Rmd
index d178ef18..4c77b693 100644
--- a/vignettes/dsl.Rmd
+++ b/vignettes/dsl.Rmd
@@ -67,3 +67,55 @@ The computed properties for the model are:
 ```{r}
 prior$properties
 ```
+
+# Calculations in the DSL
+
+Sometimes it will be useful to perform calculations in the code; you can do this with assignments.  Most trivially, giving names to numbers may help make code more understandable:
+
+```{r}
+m <- monty_dsl({
+  mu <- 10
+  sd <- 2
+  a ~ Normal(mu, sd)
+})
+```
+
+You can also use this to do things like:
+
+```{r}
+m <- monty_dsl({
+  a ~ Normal(0, 1)
+  b ~ Normal(0, 1)
+  mu <- (a + b) / 2
+  c ~ Normal(mu, 1)
+})
+```
+
+Where `c` is drawn from a normal distribution with a mean that is the average of `a` and `b`.
+
+# Pass in fixed data
+
+You can also pass in a list of data with values that should be available in the DSL code.  For example, our first example:
+
+```{r}
+prior <- monty_dsl({
+  alpha ~ Normal(178, 20)
+  beta ~ Normal(0, 10)
+  sigma ~ Uniform(0, 50)
+})
+```
+
+Might be written as
+
+```{r}
+fixed <- list(alpha_mean = 170, alpha_sd = 20,
+              beta_mean = 0, beta_sd = 10,
+              sigma_max = 50)
+prior <- monty_dsl({
+  alpha ~ Normal(alpha_mean, alpha_sd)
+  beta ~ Normal(beta_mean, beta_sd)
+  sigma ~ Uniform(0, sigma_max)
+}, fixed = fixed)
+```
+
+Values you pass in this way are **fixed** (hence the name!) and cannot be modified after the model object is created.