diff --git a/NAMESPACE b/NAMESPACE
index eab05813..855fb94a 100644
--- a/NAMESPACE
+++ b/NAMESPACE
@@ -55,6 +55,7 @@ export(batch_size)
 export(buffer)
 export(cal_method_class)
 export(cal_method_reg)
+export(circular)
 export(class_weights)
 export(conditional_min_criterion)
 export(conditional_test_statistic)
@@ -105,6 +106,7 @@ export(max_times)
 export(max_tokens)
 export(min_dist)
 export(min_n)
+export(min_points)
 export(min_times)
 export(min_unique)
 export(mixture)
@@ -142,6 +144,7 @@ export(prior_terminal_node_expo)
 export(prod_degree)
 export(prune)
 export(prune_method)
+export(radius)
 export(range_get)
 export(range_set)
 export(range_validate)
@@ -165,6 +168,9 @@ export(sample_size)
 export(scale_factor)
 export(scale_pos_weight)
 export(select_features)
+export(shared_orientation)
+export(shared_shape)
+export(shared_size)
 export(shrinkage_correlation)
 export(shrinkage_frequencies)
 export(shrinkage_variance)
@@ -216,6 +222,7 @@ export(weight)
 export(weight_func)
 export(weight_scheme)
 export(window_size)
+export(zero_covariance)
 import(rlang)
 importFrom(DiceDesign,dmaxDesign)
 importFrom(DiceDesign,lhsDesign)
diff --git a/R/param_engine_dbscan.R b/R/param_engine_dbscan.R
new file mode 100644
index 00000000..316aaaf5
--- /dev/null
+++ b/R/param_engine_dbscan.R
@@ -0,0 +1,40 @@
+#' Parameters for possible engine parameters for dbscan
+#'
+#' These parameters are used for density-based clustering methods that use the
+#' dbscan engine. They correspond to tuning parameters that would be specified using
+#' `set_engine("dbscan", ...)`.
+#'
+#' @inheritParams Laplace
+#' @details
+#'  To use these, check `?tidyclust::db_clust` to see how they are used.
+#' - `radius()` controls the radius used to determine core-points and cluster assignments
+#' - `min_points()` controls the minimum number of nearby points to be considered a core-point (including the point itself)
+#'
+#' @examples
+#' radius()
+#' min_points()
+#' @rdname dbscan_parameters
+#' @export
+radius <- function(range = c(-2, 2), trans = transform_log10()) {
+  new_quant_param(
+    type = "double",
+    range = range,
+    inclusive = c(TRUE, TRUE),
+    trans = trans,
+    label = c(radius = "Radius"),
+    finalize = NULL
+  )
+}
+
+#' @export
+#' @rdname dbscan_parameters
+min_points <- function(range = c(3L, 50L), trans = NULL) {
+  new_quant_param(
+    type = "integer",
+    range = range,
+    inclusive = c(TRUE, TRUE),
+    trans = trans,
+    label = c(min_points = "Minimum Points Threshold"),
+    finalize = NULL
+  )
+}
diff --git a/R/param_engine_mclust.R b/R/param_engine_mclust.R
new file mode 100644
index 00000000..c3be5c1a
--- /dev/null
+++ b/R/param_engine_mclust.R
@@ -0,0 +1,73 @@
+#' Parameters for possible engine parameters for mclust
+#'
+#' These parameters are used for fitting Gaussian mixture models that use the
+#' mclust engine. They correspond to tuning parameters that would be specified using
+#' `set_engine("mclust", ...)`.
+#'
+#' @param values For `circular()`, `zero_covariance()`,
+#' `shared_orientation()`, `shared_shape()`, and `shared_size()` either `TRUE` or `FALSE`.
+#' @details
+#' To use these, check `?tidyclust::gm_clust` to see how they are used.
+#' @examples
+#' circular()
+#' zero_covariance()
+#' shared_orientation()
+#' shared_shape()
+#' shared_size()
+#' @rdname mclust_parameters
+#' @export
+circular <- function(values = c(TRUE, FALSE)) {
+  new_qual_param(
+    type = "logical",
+    values = values,
+    label = c(circular = "Circular cluster shapes?"),
+    finalize = NULL
+  )
+}
+
+
+#' @export
+#' @rdname mclust_parameters
+zero_covariance <- function(values = c(TRUE, FALSE)) {
+  new_qual_param(
+    type = "logical",
+    values = values,
+    label = c(zero_covariance = "Zero covariance between predictors?"),
+    finalize = NULL
+  )
+}
+
+#' @export
+#' @rdname mclust_parameters
+shared_orientation <- function(values = c(TRUE, FALSE)) {
+  new_qual_param(
+    type = "logical",
+    values = values,
+    label = c(shared_orientation = "Shared orientation between clusters?"),
+    finalize = NULL
+  )
+}
+
+#' @export
+#' @rdname mclust_parameters
+shared_shape <- function(values = c(TRUE, FALSE)) {
+  new_qual_param(
+    type = "logical",
+    values = values,
+    label = c(shared_shape = "Same shape for all clusters?"),
+    finalize = NULL
+  )
+}
+
+
+#' @export
+#' @rdname mclust_parameters
+shared_size <- function(values = c(TRUE, FALSE)) {
+  new_qual_param(
+    type = "logical",
+    values = values,
+    label = c(shared_size = "Same size for all clusters?"),
+    finalize = NULL
+  )
+}
+
diff --git a/_pkgdown.yml b/_pkgdown.yml
index 9ab8a7e9..280da31c 100644
--- a/_pkgdown.yml
+++ b/_pkgdown.yml
@@ -101,16 +101,23 @@ reference:
   - title: Parameter objects for specific model engines
     contents:
     - bart-param
+    - circular
     - conditional_min_criterion
     - confidence_factor
     - extrapolation
     - max_nodes
     - max_num_terms
+    - min_points
     - num_leaves
+    - radius
     - regularization_factor
     - rule_bands
     - scale_pos_weight
+    - shared_orientation
+    - shared_shape
+    - shared_size
     - shrinkage_correlation
+    - zero_covariance
 
   - title: Parameter objects for post-processing
     contents:
diff --git a/man/dbscan_parameters.Rd b/man/dbscan_parameters.Rd
new file mode 100644
index 00000000..d8059707
--- /dev/null
+++ b/man/dbscan_parameters.Rd
@@ -0,0 +1,37 @@
+% Generated by roxygen2: do not edit by hand
+% Please edit documentation in R/param_engine_dbscan.R
+\name{radius}
+\alias{radius}
+\alias{min_points}
+\title{Parameters for possible engine parameters for dbscan}
+\usage{
+radius(range = c(-2, 2), trans = transform_log10())
+
+min_points(range = c(3L, 50L), trans = NULL)
+}
+\arguments{
+\item{range}{A two-element vector holding the \emph{defaults} for the smallest and
+largest possible values, respectively. If a transformation is specified,
+these values should be in the \emph{transformed units}.}
+
+\item{trans}{A \code{trans} object from the \code{scales} package, such as
+\code{scales::transform_log10()} or \code{scales::transform_reciprocal()}. If not provided,
+the default is used which matches the units used in \code{range}. If no
+transformation, \code{NULL}.}
+}
+\description{
+These parameters are used for density-based clustering methods that use the
+dbscan engine. They correspond to tuning parameters that would be specified using
+\code{set_engine("dbscan", ...)}.
+}
+\details{
+To use these, check \code{?tidyclust::db_clust} to see how they are used.
+\itemize{
+\item \code{radius()} controls the radius used to determine core-points and cluster assignments
+\item \code{min_points()} controls the minimum number of nearby points to be considered a core-point (including the point itself)
+}
+}
+\examples{
+radius()
+min_points()
+}
diff --git a/man/dials-package.Rd b/man/dials-package.Rd
index 64667afe..e55736d9 100644
--- a/man/dials-package.Rd
+++ b/man/dials-package.Rd
@@ -53,7 +53,7 @@ Authors:
 
 Other contributors:
 \itemize{
-  \item Posit Software, PBC (\href{https://ror.org/03wc8by49}{ROR}) [copyright holder, funder]
+  \item Posit Software, PBC (03wc8by49) [copyright holder, funder]
 }
 
 }
diff --git a/man/mclust_parameters.Rd b/man/mclust_parameters.Rd
new file mode 100644
index 00000000..adae8606
--- /dev/null
+++ b/man/mclust_parameters.Rd
@@ -0,0 +1,39 @@
+% Generated by roxygen2: do not edit by hand
+% Please edit documentation in R/param_engine_mclust.R
+\name{circular}
+\alias{circular}
+\alias{zero_covariance}
+\alias{shared_orientation}
+\alias{shared_shape}
+\alias{shared_size}
+\title{Parameters for possible engine parameters for mclust}
+\usage{
+circular(values = c(TRUE, FALSE))
+
+zero_covariance(values = c(TRUE, FALSE))
+
+shared_orientation(values = c(TRUE, FALSE))
+
+shared_shape(values = c(TRUE, FALSE))
+
+shared_size(values = c(TRUE, FALSE))
+}
+\arguments{
+\item{values}{For \code{circular()}, \code{zero_covariance()},
+\code{shared_orientation()}, \code{shared_shape()}, and \code{shared_size()} either \code{TRUE} or \code{FALSE}.}
+}
+\description{
+These parameters are used for fitting Gaussian mixture models that use the
+mclust engine. They correspond to tuning parameters that would be specified using
+\code{set_engine("mclust", ...)}.
+}
+\details{
+To use these, check \code{?tidyclust::gm_clust} to see how they are used.
+}
+\examples{
+circular()
+zero_covariance()
+shared_orientation()
+shared_shape()
+shared_size()
+}
diff --git a/tests/testthat/test-params.R b/tests/testthat/test-params.R
index b71f5c41..480810f0 100644
--- a/tests/testthat/test-params.R
+++ b/tests/testthat/test-params.R
@@ -137,11 +137,13 @@ test_that("param ranges", {
   expect_equal(target_weight(c(0.1, 0.4))$range, list(lower = 0.1, upper = 0.4))
   expect_equal(lower_limit(c(Inf, 0))$range, list(lower = Inf, upper = 0))
   expect_equal(upper_limit(c(0, Inf))$range, list(lower = 0, upper = Inf))
-  expect_equal(max_num_terms(c(31, 100))$range, list(lower = 31, upper = 100))
-  expect_equal(max_nodes(c(31, 100))$range, list(lower = 31, upper = 100))
-  expect_equal(num_tokens(c(31, 100))$range, list(lower = 31, upper = 100))
-  expect_equal(mtry_prop(c(.1, .2))$range, list(lower = .1, upper = .2))
-  expect_equal(dropout(c(.1, .2))$range, list(lower = .1, upper = .2))
+  expect_equal(max_num_terms(c(31,100))$range, list(lower = 31, upper = 100))
+  expect_equal(max_nodes(c(31,100))$range, list(lower = 31, upper = 100))
+  expect_equal(num_tokens(c(31,100))$range, list(lower = 31, upper = 100))
+  expect_equal(mtry_prop(c(.1,.2))$range, list(lower = .1, upper = .2))
+  expect_equal(dropout(c(.1,.2))$range, list(lower = .1, upper = .2))
+  expect_equal(radius(c(0.01, 100))$range, list(lower = 0.01, upper = 100))
+  expect_equal(min_points(c(3, 50))$range, list(lower = 3, upper = 50))
 })
 
 
@@ -178,4 +180,9 @@ test_that("param values", {
   expect_equal(all_neighbors(TRUE)$values, TRUE)
   expect_equal(cal_method_class()$values, values_cal_cls)
   expect_equal(cal_method_reg()$values, values_cal_reg)
+  expect_equal(circular(TRUE)$values, TRUE)
+  expect_equal(zero_covariance(TRUE)$values, TRUE)
+  expect_equal(shared_orientation(TRUE)$values, TRUE)
+  expect_equal(shared_shape(TRUE)$values, TRUE)
+  expect_equal(shared_size(TRUE)$values, TRUE)
 })